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Journal articles on the topic 'Contraction mapping and fixed point'

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Published: 7 June 2025

Last updated: 16 July 2025

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1

C. Ushabhavani. "On Certain Fixed Points for (α,φ,F)-Contraction on S_b- Metric Spaces with Applications". Advances in Nonlinear Variational Inequalities 27, № 2 (2024): 360–74. http://dx.doi.org/10.52783/anvi.v27.972.

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This work establishes unique fixed point theorems (UFPT) for self mapping in complete S_b-metric spaces (S_b-MS) with the concept of (α,φ,F)-contraction in the context of S_b-MS Furthermore, we show how the results may be used and present applications to integral equations and homotopy theory. Introduction: In previous work authors were discussed fixed pointon various metric spaces with F -contractions, α-type almost -F- contractions, α-type F -Suzuki contractions, (φ, F)-contraction, F - weak contractions, α −ψ-contractive type, α −ψ-Meir-Keeler contractive mapping, α-ratonal contractive mapp

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2

Kavvampalli Jyothirmayi Rani. "Some Applications via Coupled Fixed Point Theorems for (????, ????)-H-Contraction Mappings in Partial b- Metric Spaces." Communications on Applied Nonlinear Analysis 31, no. 5s (2024): 351–71. http://dx.doi.org/10.52783/cana.v31.1055.

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This work establishes unique common coupled fixed point theorems for given mapping in complete partial b-metric spaces with the concept of (α, ϕ)-H-contraction in the context of partial b-metric spaces. (α, ϕ)-H-contraction Furthermore, we show how the results may be used and present applications to integral equations and Homotopy theory. Introduction In previous work, authors have discussed various fixed point theorems on partial b-metric spaces with (ψ, ϕ)-weakly contractive mappings, α−ψ-contractive type, Suzuki type contractions, rational contraction and H-weak contractions. In our work, w

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3

K. Varalakshmi. "Fixed Point Results in G Metric Space via Α-Series". Communications on Applied Nonlinear Analysis 32, № 6s (2025): 275–89. https://doi.org/10.52783/cana.v32.3294.

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Introduction: Mustafa and sims [1] introduced the concept of G-metric space in 2005. Afterwards, Mustafa et al and many authors [3]-[19] obtained some common fixed-point theorems, coupled and tripled fixed point results for mappings satisfying different contractive conditions in G metric space. In this study we prove fixed point results in G metric space via α-series by using some conditions that are a sequence of a mappings and a self-mapping. Objectives: To show tripled fixed-point theorems and common fixed point theorems by using sequence of mappings and self a self-mapping via α-series and

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NITHIARAYAPHAKS, WORAPHAK, and WUTIPHOL SINTUNAVARAT. "On approximating fixed points of weak enriched contraction mappings via Kirk's iterative algorithm in Banach spaces." Carpathian Journal of Mathematics 39, no. 2 (2022): 423–32. http://dx.doi.org/10.37193/cjm.2023.02.07.

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Recently Berinde and Păcurar [Approximating fixed points of enriched contractions in Banach spaces. {\em J. Fixed Point Theory Appl.} {\bf 22} (2020), no. 2., 1--10], first introduced the idea of enriched contraction mappings and proved the existence of a fixed point of an enriched contraction mapping using the well-known fact that any fixed point of {the averaged mapping $T_\lambda$, where $\lambda\in (0,1]$, is also a fixed point of the initial mapping $T$}. In this work, we introduce the idea of weak enriched contraction mappings, and a new generalization of an averaged mapping called doubl

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5

Babenko, V. F., V. V. Babenko, and O. V. Kovalenko. "Fixed sets and fixed points for mappings in generalized $\rm Lim$-spaces of Fréchet." Carpathian Mathematical Publications 15, no. 1 (2023): 260–69. http://dx.doi.org/10.15330/cmp.15.1.260-269.

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In the article, we axiomatically define generalized $\rm Lim$-spaces $(X,{\rm Lim})$, Cauchy structures, contractive mappings and prove an abstract version of the contraction mapping principle. We also consider ways to specify families of Cauchy sequences and contraction conditions using a base in $X^2$, distance-like or sum-like functions with values in some partially ordered set $Y$. We establish fixed set and fixed point theorems for generalized contractions of the Meir-Keeler and Taylor, Ćirić and Caristi types. The obtained results generalize many known fixed point theorems and are new ev

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6

Chakar, Randa, Sofiane Dehilis, Wassim Merchela та Hamza Guebbai. "ρ-F-contraction fixed point theorem". Russian Universities Reports. Mathematics, № 148 (2024): 485–93. https://doi.org/10.20310/2686-9667-2024-29-148-485-493.

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In this paper, we study the question of conditions for the existence and uniqueness of a fixed point of a mapping over a complete metric space. We first discuss the concepts of F- contraction and F^*-contraction in fixed point theory. These concepts, developed respectively by Wardowski and Piri with Kumam, have catalyzed significant research in various metric spaces. We then propose a generalization of these concepts, ρ-F-contraction and ρ-F^*-contraction, and demonstrate its effectiveness in ensuring the existence and uniqueness of fixed points. This new approach provides greater flexibility

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7

Fulga, Andreea, and Erdal Karapınar. "Revisiting of some outstanding metric fixed point theorems via E-contraction." Analele Universitatii "Ovidius" Constanta - Seria Matematica 26, no. 3 (2018): 73–98. http://dx.doi.org/10.2478/auom-2018-0034.

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AbstractIn this paper, we introduce the notion of α-ψ-contractive mapping of type E, to remedy of the weakness of the existing contraction mappings. We investigate the existence and uniqueness of a fixed point of such mappings. We also list some examples to illustrate our results that unify and generalize the several well-known results including the famous Banach contraction mapping principle.

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8

Ciric, Ljubomir, Sumit Chandok, and Mujahid Abbas. "Invariant approximation results of generalized contractive mappings." Filomat 30, no. 14 (2016): 3875–83. http://dx.doi.org/10.2298/fil1614875c.

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Abbas, Ali and Salvador [Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl. 2013, 2013:243] extended the concept of F- contraction mapping introduced in [21], to two mappings. The aim of this paper is to introduce the notion of a generalized F1- weak contraction mapping and to study sufficient conditions for the existence of common fixed points for such class of mappings. As applications, related invariant approximation results are derived. The results obtained herein unify, generalize and complement various known results in the literature.

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9

V. Rajitha. "Tripled Fixed Point Results in G_b-Metric Spaces." Communications on Applied Nonlinear Analysis 31, no. 8s (2024): 433–40. http://dx.doi.org/10.52783/cana.v31.1536.

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In recent work authors were discussed fixed point results with various contractions like (ψ,ϕ)-weakly contractive mappings, cyclic contraction, E.A property, Suzuki-type contraction etc. in complete -metric spaces, With the help of completeness property and continuous function we obtained unique tripled fixed point in -metric spaces. Objectives: To show tripled fixed point theorems in -metric spaces via new type of contraction and shown illustrate an example which supports the main result. Methods: In recent work authors were discussed fixed point results with various contractions like (ψ, ϕ)-

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10

Muhammad, Rafique, Mohammed Shagari, and Akbar Azam. "On interpolative fuzzy contractions with applications." Filomat 37, no. 1 (2023): 207–19. http://dx.doi.org/10.2298/fil2301207m.

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In this paper, following a new interpolation approach in fixed point theory, we introduce the concepts of interpolative Hardy-Rogers-type fuzzy contraction and interpolative Reich-Rus-Ciric type fuzzy contraction in the framework of metric spaces, and we analyze the existence of fuzzy fixed points for such contractions equipped with some suitable hypotheses. A few consequences in single-valued mappings which include the conclusion of the main result of Karapinar et al. [On interpolative Hardy-Rogers type contractions. Symmetry, 2019, 11(1), 8] are obtained. On the basis that fixed point of a s

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11

Vincent, Koech, Musundi W. Sammy, and Kinyanjui Jeremiah. "Derivation of Fixed-Point Theorem Using Expansive Mapping Approach." Asian Research Journal of Mathematics 19, no. 8 (2023): 103–7. http://dx.doi.org/10.9734/arjom/2023/v19i8692.

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Application of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that if T:X→X is a contraction mapping on a complete metric space (X, d) then there exists a unique fixed point in X. A lot has been done on application of contraction mapping in Fixed Point Theorem on metric spaces such as Cantor set with the contraction constant of 1/3 , the Sierpinski triangle also with contraction constant of 1/2 . On the other hand, a mapping T:X → X on (X, d) such that ∀x, y ∈ X: d(Tx, Ty) ≥ d (x, y) is called an expansive mapping. There

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12

DEY, LEKHA, and Sanjay Sharma. "FIXED POINT RESULT USING TWO DOMINATED MAPPING ON A CLOSED BALL." International Journal of Scientific Research in Modern Science and Technology 2, no. 12 (2023): 38–47. http://dx.doi.org/10.59828/ijsrmst.v2i12.165.

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In the present work, we obtain the result of fixed-point theorem through quasi-contraction mapping and improve the work of A. Shoaib et.al (2015) in a left and right K-sequentially 0-complete ordered quasi-partial spaces respectively, where locally contractive condition satisfied on a closed set. We can use this result to solve the complication of computer algorithms and study it. In this paper, some fixed-point results of self-mapping which is defined on quasi partial metric spaces are given by using dominated mapping (A. Shoaib et.al, 2015) in a left and right K-sequentially 0-complete order

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13

Roy, Kushal, and Sayantan Panja. "From interpolative contractive mappings to generalized Ciric-quasi contraction mappings." Applied General Topology 22, no. 1 (2021): 109. http://dx.doi.org/10.4995/agt.2021.14045.

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<p>In this article we consider a restricted version of Ciric-quasi contraction mapping for showing that this mapping generalizes several known interpolative type contractive mappings. Also here we introduce the concept of interpolative strictly contractive type mapping T and prove a fixed point theorem for such mapping over a T-orbitally compact metric space. Some examples are given in support of our established results. Finally we give an observation regarding (λ, α, β)-interpolative Kannan contractions introduced by Gaba et al.</p>

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14

Eshi, Dakjum, Bipan Hazarika, Nipen Saikia, et al. "On Some Ciric Type Cyclic Coupled F-Contractions in Complete Metric Spaces." International Journal of Analysis and Applications 23 (April 21, 2025): 97. https://doi.org/10.28924/2291-8639-23-2025-97.

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In this paper, the notions of cyclic coupled Wardowski’s F-contraction and generalized Ciric type mappings in complete metric space are discussed. Some coupled cyclic F-contractions of generalized Ciric type mappings are defined, and existence results for coupled fixed point, coupled coincidence point, strong coupled fixed point, and coupled best proximity point are established in the framework of complete metric space. An existence result for a coupled fixed point for generalized Ciric-type cyclic coupled F-contractive multivalued mapping is established. Further, an application of our result

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15

Khan, Abdul Rahim, Hamed H. Al-Sulami, Muhammad Rashid, and Faiza Shabbir. "Fixed points of multivalued convex contractions with application." PLOS One 20, no. 5 (2025): e0321860. https://doi.org/10.1371/journal.pone.0321860.

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In this work, we establish fixed point outcomes for single- valued convex contraction type mappings in the context of a b-metric space. Some of the new results are extended for a multivalued convex contraction and an F-convex contraction. Thereby, an analogue of the famous Nadler’s fixed point theorem for a multivalued convex contraction mapping is obtained. The relation among various contractions is presented in a diagram for an insight in this area of investigations. We apply a special case of Theorem 2.11, to solve a nonlinear Fredholm integral equation for a Chatterjea convex contraction.

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16

Errai, Youssef, El Miloudi Marhrani, and Mohamed Aamri. "Some New Results of Interpolative Hardy–Rogers and Ćirić–Reich–Rus Type Contraction." Journal of Mathematics 2021 (May 20, 2021): 1–12. http://dx.doi.org/10.1155/2021/9992783.

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In this paper, we present new concepts on completeness of Hardy–Rogers type contraction mappings in metric space to prove the existence of fixed points. Furthermore, we introduce the concept of g -interpolative Hardy–Rogers type contractions in b -metric spaces to prove the existence of the coincidence point. Lastly, we add a third concept, interpolative weakly contractive mapping type, Ćirić–Reich–Rus, to show the existence of fixed points. These results are a generalization of previous results, which we have reinforced with examples.

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17

Raji, Muhammed, та Musa Adeku Ibrahim. "Fixed point theorems for modified F-weak contractions via α-admissible mapping with application to periodic points". Annals of Mathematics and Computer Science 20 (3 січня 2024): 82–97. http://dx.doi.org/10.56947/amcs.v20.232.

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In (Fixed Point Theory Appl. 94:6, 2012), Wardowski introduced a new type of contraction called F-contraction and proved a fixed point result in complete metric spaces, which in turn generalizes the Banach contraction principle. The aim of this paper is to introduce a modified -F-weak contractions with respect to a self-mapping on a metric space and to obtain fixed point results. Examples are provided to support results and concepts presented herein. As an application of our results, periodic point results for the F-contractions in metric spaces are proved.

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18

Ajay Kumar Chaudhary. "Extension and Generalization of Banach Contraction in Metric and in Menger Space." Communications on Applied Nonlinear Analysis 32, no. 2 (2024): 53–63. http://dx.doi.org/10.52783/cana.v32.1707.

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The root of metric fixed point theory is Stefen Banach's contraction mapping, a research source for shrinking the distance between two points in space. As a source, many authors have introduced many contraction mappings as extensions and generalizations of Banach contraction and established fixed point theorems under the property that each such mapping in complete metric and Menger space has a unique fixed point. This article presents updated results of Banach contraction generalization and extension forms in metric and Menger space which helps the comparative and interrelationship study in th

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19

Hassnain, Syed Irtaza, and Wutiphol Sintunavarat. "Elegant Rational Contractive Conditions with Applications to Implicit Functional Integral Equations." Bangmod International Journal of Mathematical and Computational Science 11 (June 25, 2025): 157–83. https://doi.org/10.58715/bangmodjmcs.2025.11.8.

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This paper aims to introduce several new classes of contraction mappings inspired by convex and rational contraction mappings. We establish the existence and uniqueness of fixed points for each newly proposed contraction mapping in metric spaces. To validate our theoretical findings, we provide several illustrative examples that demonstrate cases where well-known fixed point results, such as the Banach contraction principle, the Kannan fixed point theorem, the Chatterjea fixed point theorem, the Jaggi fixed point theorem, and the Istratescu fixed point theorem, are not applicable. As an applic

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20

Sager, Nilay, and Birsen Sağır. "Common fixed, coupled coincidence and common coupled fixed point results in hyperbolic valued metric spaces." Boletim da Sociedade Paranaense de Matemática 41 (December 23, 2022): 1–15. http://dx.doi.org/10.5269/bspm.51825.

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In this paper, we obtain existence of unique common fixed point for a contraction mapping on hyperbolic valued metric spaces, and also develop some coupled coincidence point and common coupled fixed point results for two mappings satisfying various contractive conditions in such spaces. We also give some illustrative examples to validate our results.

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21

Qawasmeh, Tariq. "(H, Ωb)-Interpolative Contractions in Ωb-distance Mappings with Application". European Journal of Pure and Applied Mathematics 16, № 3 (2023): 1717–30. http://dx.doi.org/10.29020/nybg.ejpam.v16i3.4819.

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Interpolative Kannan contractions are a refinement of Kannan contraction, which is considered as one of the significant notions in fixed point theory. Gb-metric spaces is considered as a generalized concept of both concepts b-metric and G-metric spaces therefore, the significant fixed and common fixed point results of the contraction based on this concept is generalized resultsfor both concepts. The purpose of this manuscript, is to take advantage to interpolative Kannan contraction together with the notion of Ωb which equipped with Gb-metric spaces and H simulation functions to formulate two

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22

Subrahmanyam, P. V., and I. L. Reilly. "Some fixed point theorems." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 53, no. 3 (1992): 304–12. http://dx.doi.org/10.1017/s144678870003648x.

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AbstractBanach's contraction principle guarantees the existence of a unique fixed point for any contractive selfmapping of a complete metric space. This paper considers generalizations of the completeness of the space and of the contractiveness of the mapping and shows that some recent extensions of Banach's theorem carry over to spaces whose topologies are generated by families of quasi-pseudometrics.

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23

Alqahtani, Badr, Andreea Fulga, and Erdal Karapınar. "A Fixed Point Result with a Contractive Iterate at a Point." Mathematics 7, no. 7 (2019): 606. http://dx.doi.org/10.3390/math7070606.

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In this manuscript, we define generalized Kincses-Totik type contractions within the context of metric space and consider the existence of a fixed point for such operators. Kincses-Totik type contractions extends the renowned Banach contraction mapping principle in different aspects. First, the continuity condition for the considered mapping is not required. Second, the contraction inequality contains all possible geometrical distances. Third, the contraction inequality is formulated for some iteration of the considered operator, instead of the dealing with the given operator. Fourth and last,

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24

Tejal, Gore1 Rohini Gore*2. "Common Fixed Point Theorems In G-Metric Spaces for Weakly Mapping by Using Contraction Condition." International Journal of Scientific Research and Technology 2, no. 3 (2025): 86–89. https://doi.org/10.5281/zenodo.14959503.

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In this paper, we studied common fixed point theorems in G-metric spaces. We establish several fixed point theorems for single and multi-valued mappings in G-metric spaces, including Banach, Kannan, Chatterjea type contractions. The main result is fixed point theorem in compact G- metric spaces for weakly mapping by using contraction condition. Our results provide a unified framework for studying the existence and uniqueness of fixed points in G-metric spaces, and have applications in various fields such as mathematics, physics, and engineering.

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25

Afifah Hayati. "SOME COINCIDENCE POINT THEOREMS IN MODULAR SPACES." Mathline : Jurnal Matematika dan Pendidikan Matematika 7, no. 1 (2022): 91–109. http://dx.doi.org/10.31943/mathline.v7i1.260.

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In metric spaces, there are quasi-contraction mappings and Suzuki-contraction mapping, that are generalization of contraction mappings. In this article, we give coincidence point theorems of quasi-contraction mappings and Suzuki-contraction mappings in modular spaces, that are generalizations of fixed point theorem of quasi-contractraction mappings and Suzuki-contraction theorem in modular spaces.

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26

Choudhury, Binayak S., Nikhilesh Metiya, T. Som, and Sunirmal Kundu. "Existence and stability results for fixed points of multivalued $F$ contractions and application to Volterra type non homogeneous integral equation of second kind." Annals of the University of Craiova Mathematics and Computer Science Series 50, no. 1 (2023): 1–15. http://dx.doi.org/10.52846/ami.v50i1.1597.

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In this paper we introduce multivalued modified F-contraction on a metric space. This is a multivalued mapping obtained by incorporating the idea of the recently introduced F-contraction which has attracted much attention in contemporary research. We explore the fixed point problem associated with the above contractive mapping. We also investigate the data dependence and stability properties of the fixed point sets associated with these multivalued contractions. We discuss an illustration of the main result and present an application of the single valued version of the main theorem to a proble

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27

Chavan, Swati Ankush, and Varsha D. Borgaonkar. "Some Fixed Point Results on Compact Metric Spaces." International Scientific Journal of Engineering and Management 04, no. 04 (2025): 1–7. https://doi.org/10.55041/isjem02606.

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Abstract: This paper aims to study some generalized fixed-point results in a compact metric space. It mainly focuses on the existence and uniqueness of fixed point of self-mappings on a metric space and its generalizations. This paper uses iterative techniques to show the existence of a unique fixed point for a self-mapping satisfying certain generalized contractive conditions. Keywords: Compact Space, Metric Space Contraction, Fixed Point, Convergence sequence.

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28

Chand, Deep, Yumnan Rohen, and Nicola Fabiano. "Paired-Kannan contraction mappings and fixed point results." Gulf Journal of Mathematics 17, no. 2 (2024): 136–54. http://dx.doi.org/10.56947/gjom.v17i2.2185.

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We introduce a novel contraction concept for mappings within metric spaces called Paired-Kannan contraction. Unlike traditional Kannan contraction mappings, which involve two points, Paired-Kannan contraction mappings extend this concept to three points. We explore their properties, noting that while these mappings may generally be discontinuous, they exhibit continuity at fixed points akin to Kannan contractions. Importantly, we establish that Paired-Kannan contraction mappings constitute distinct entities from traditional Kannan contractions. We prove a fixed point theorem for Paired Kannan

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29

Wongsasinchai, Paiwan, and Warut Kitcharoen. "GENERALIZED QUASI-CONTRACTION FOR DISLOCATED QUASI-METRIC SPACES." Journal of Inequalities and Special Functions 14, no. 3 (2023): 7–16. https://doi.org/10.54379/jiasf-2023-3-2.

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In this paper, T-orbitally complete dislocated quasi-metric spaces are utilized to validate fixed point results for freshly developed Geraghty quasi-contraction type mappings. The Geraghty quasi-contraction type mappings generalize Ciric’s quasi-contraction mappings and other Geraghty quasicontractive type mappings in the literature. Without establishing a continuity condition on the mapping, fixed point results are obtained, generalizing some relevant work in the literature.

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30

Bansal, Dinesh Rani, and Reetu Reetu. "Common Fixed Point Theorems Involving Cubic Terms of d(x, y) in b-Metric Spaces." Indian Journal Of Science And Technology 18, no. 3 (2025): 184–92. https://doi.org/10.17485/ijst/v18i3.1590.

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Objective/Aim: To establish the existence and uniqueness of fixed points for self maps in b-metric spaces. Methods: We have used generalized 𝜑-weak contractive condition involving cubic terms of d(x, y) and weak compatibility of two maps in the setting of b-metric spaces. Findings: Some fixed point theorems for a self map and common fixed point theorems for two maps have been proved and some suitable examples are also given to justify the proven results. Novelty: In b-metric spaces, the existence of fixed points for mappings satisfying generalized 𝜑-weak contractive conditions involving cubic

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31

Patel, Uma Devi, Vineeta Chandra, Milica Savatović, and Stojan Radenović. "On k-fuzzy metric spaces with applications." Nonlinear Analysis: Modelling and Control 30 (January 2, 2025): 1–22. https://doi.org/10.15388/namc.2025.30.38313.

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With application point of view, Gopal et al. [D. Gopal, W. Sintunavarat, A.S. Ranadive, S. Shukla, The investigation of k-fuzzy metric spaces with the first contraction principle in such spaces, Soft Comput., 27:11081–11089, 2023] generalized the conceptions of a fuzzy metric space and introduced the definition of k-fuzzy metric space. Here a fuzzy set defined in k-fuzzy metric space is a membership function FY : X × X × (0, +∞)k -> [0; 1], that is, the fuzzy distance between two points of the set depends on more than one parameter, and then also introduced first contraction principle in th

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32

Manjusha, P. Gandhi, B. Bajpai Kavita, and A. Aserkar Anushree. "A study of k- Contraction and the Triangular a Orbital Admissibility Condition in Quasi-metric Space." Indian Journal of Science and Technology 16, no. 44 (2023): 3978–81. https://doi.org/10.17485/IJST/v16i44.1430.

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Abstract <strong>Objective:</strong> To establish the presence of fixed point under a novel contraction condition and a freshly defined distance function, we harness the concept of triangular orbital admissible mappings. <strong>Method:</strong> Consider two mapping in quasi-metric space. These two mapping satisfy a new contraction condition and also the triangular orbital admissible condition. Define the sequences for two mappings. Consider two cases for odd and even sequences. Show that a fixed point is common for two mappings and then demonstrate its uniqueness. <strong>

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Jain, Kapil, Jatinderdeep Kaur, and Satvinder Singh Bhatia. "Fixed Points of \(\xi\) - (\(\alpha\), \(\beta\))- Contractive Mappings in b-Metric Spaces." Journal of Advances in Mathematics and Computer Science 38, no. 6 (2023): 6–15. http://dx.doi.org/10.9734/jamcs/2023/v38i61764.

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In the paper [Some new observations on Geraghty and \(\acute{C}\)iri\(\acute{c}\) type results in b-metric spaces, Mathematics, 7, (2019), doi: 10.3390/math7070643] Mlaiki et al. introduced (\(\alpha\), \(\beta\))-type contraction in order to generalize the contraction mapping defined by Pant and Panicker. Also, in the paper [Some fixed point results in b- metric spaces and b-metric-like spaces with new contractive mappings, Axioms, 10(2), (2021), 15 pages, doi: 10.3390/axioms10020055] Jain and Kaur presented the concepts of \(\xi\) -contractive mappings. Now, the aim of the present article is

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34

Benmezaï, Abdelhamid, Karima Hammache, and Nassima Melouane. "Fixed Point Index for Simulation Mappings and Applications." Analele Universitatii "Ovidius" Constanta - Seria Matematica 31, no. 3 (2023): 27–45. https://doi.org/10.2478/auom-2023-0030.

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Abstract In this paper, we construct the fixed point index for a class of contractive mapping defined by a simulation mapping and a measure of noncompact-ness noted by Z µ − contraction maps. Then we establish some fixed point theorem for this mapping of the Krasnoselskii type. An Application to the integral equation is presented to support the results.

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Işık, Hüseyİn, Hassen Aydi, Mohd Salmi Md Noorani, and Haitham Qawaqneh. "New Fixed Point Results for Modified Contractions and Applications." Symmetry 11, no. 5 (2019): 660. http://dx.doi.org/10.3390/sym11050660.

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In this study, we introduce a new type of contractive mapping to establish the existence and uniqueness of fixed points for this type of contraction. Some related examples are built demonstrating the superiority of our results compared to the existing onesin the literature. As applications of the results obtained, some new fixed point theorems are presented for graph-type contractions. Furthermore, sufficient conditions are discussed to ensure the existence underlying various approaches of a solution for a functional equation originating in dynamic programming.

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GOYAL, A. K., and Gaurav Kumar Garg. "Common Fixed Point Theorem For Rational Expressions In 2-Banach Spaces." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10, no. 2 (2019): 1101–4. http://dx.doi.org/10.61841/turcomat.v10i2.13822.

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The study of non-contraction mapping concerning the existence of fixed points draws attention of various authors in non-linear analysis. Gahlar [6] introduced the concept of 2- Banach spaces. Badshah and Gupta [3] , Yadava, Rajput, Choudhary and Bhardwaj [26] proved some results on fixed point in 2-Banach spaces. Recently Yadava,Rajput, Bhardwaj [25] proved a result on fixed point in 2- Banach spaces for non- contraction mappings. In this paper we prove some common fixed point theorems for non-contraction mappings in 2-Banach spaces, which contains new rational expressions. 2010 AMS Mathematic

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37

Abbas, Mujahid, Basit Ali, and Salvador Romaguera. "Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/391952.

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Wardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalizedF-contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces. Some theorems on invariant approximations in normed linear spaces are also deduced. Our results extend, unify, and generalize comparable results in the literature.

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Kumar, Anil. "FIXED POINT THEOREM FOR F-KANNAN MAPPING." jnanabha 54, no. 01 (2024): 262–69. http://dx.doi.org/10.58250/jnanabha.2024.54131.

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39

Kumar Garg, Arun, and Bharti Mishra. "Fixed Point for Contraction Mapping in Complete Parametric B Metric Space." International Journal of Science and Research (IJSR) 11, no. 8 (2022): 677–80. http://dx.doi.org/10.21275/sr22805110136.

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Pant, R. P. "An Extended Kannan Contraction Mapping and Applications." International Journal of Mathematical, Engineering and Management Sciences 9, no. 4 (2024): 931–42. http://dx.doi.org/10.33889/ijmems.2024.9.4.049.

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We extend the Kannan contraction principle and obtain a result that holds for both contractive and non-expansive mappings. Such mappings admit multiple fixed-points and the fixed-point sets and domains of these mappings display interesting algebraic, geometric and dynamical features. Since contraction mappings admit only one fixed-point, almost all the existing results on contractive mappings can be generalized in the light of our theorem. As an application of our main theorem, we obtain the integral solutions of a nonlinear Diophantine equation; the solutions are Pythagorean triples, which re

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Sabri, Raghad I., та Buthainah A. Ahmed. "Best proximity point results for generalization of 𝜶̌–𝜼̌ proximal contractive mapping in fuzzy banach spaces". Indonesian Journal of Electrical Engineering and Computer Science 28, № 3 (2022): 1451–62. https://doi.org/10.11591/ijeecs.v28.i3.pp1451-1462.

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The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems provide an approximate solution to the fixed-point equation Tҳ = ҳ. It is used to solve the problem to determine an approximate solution that is optimum. The main goal of this paper is to present new types of proximal contraction for nonself mappings in a fuzzy Banach space. At first, the notion of the best proximity point is presented. We introduce the notion of 𝛼̌–𝜂̌-𝛽̌ proximal contractive. After that, the best proximit

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42

Kutbi, M. A., N. Hussain, and S. Khaleghizadeh. "NewPPFDependent Fixed Point Theorems for Suzuki TypeGF-Contractions." Journal of Function Spaces 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/136306.

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We introduce new concepts of anαc-GF-contractive nonself-mapping, a weakαc-GF-contractive nonself-mapping, a generalizedαc-GF-contractive nonself-mapping, and Suzuki typeGF-contractions and establish the existence ofPPFdependent fixed point theorems for such kind of contractive nonself-mappings in the Razumikhin class. As applications of our results, we derive somePPFdependent fixed point theorems forGF-contractive nonself-mappings whenever the range space is endowed with a graph or a partial order. The obtained results generalize, extend, and modify somePPFdependent fixed point results in the

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Raji, Muhammed, and Musa Adeku Ibrahim. "AN APPROACH TO THE STUDY OF FIXED POINT THEORY IN HILBERT SPACE." JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES 11, no. 01 (2023): 115–26. http://dx.doi.org/10.56827/jrsmms.2023.1101.8.

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The purpose of this article is to extend Banach’s contraction principle through a new rational expression in the contractive condition to establish the existence and uniqueness of fixed point of a closed subset of Hilbert space to a self mapping. The result is extended to a pair of self mappings and positive integers powers of a pair mapping and further extended to a sequence of mappings in the space. The presented results extend and generalized various known comparable results from the current literature.

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44

Ren, Yijie, Junlei Li, and Yanrong Yu. "Common Fixed Point Theorems for Nonlinear Contractive Mappings in Dislocated Metric Spaces." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/483059.

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In 1986, Matthews generalized Banach contraction mapping theorem in dislocated metric space that is a wider space than metric space. In this paper, we established common fixed point theorems for a class of contractive mappings. Our results extend the corresponding ones of other authors in dislocated metric spaces.

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45

Rani, Bhumika, Jatinderdeep Kaur, and Satvinder Singh Bhatia. "On the Fixed Points of Large Enriched Contractions in Convex Metric Space with an Application." Symmetry 17, no. 5 (2025): 748. https://doi.org/10.3390/sym17050748.

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This paper investigates the fixed points of large enriched contractions in a convex metric space as well as in a convex G-metric space. We establish the sufficient conditions for the existence and uniqueness of fixed points for these mappings. We use the Kransnoselskij-type iterative procedure for the approximation of these fixed points in complete convex metric spaces. We demonstrate that the Kransnoselskij-type iterative approach converges to the unique fixed point associated with large enriched contractions. Our results extend and generalize classical fixed point results by introducing this

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I. Sabri, Raghad, та Buthainah A. Ahmed. "Best Proximity Point Results for Generalization of α ̌–η ̌ Proximal Contractive Mapping in Fuzzy Banach Spaces". Indonesian Journal of Electrical Engineering and Computer Science 28, № 3 (2022): 1451. http://dx.doi.org/10.11591/ijeecs.v28.i3.pp1451-1462.

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<p>The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems provide an approximate solution to the fixed-point equation Tҳ = ҳ. It is used to solve the problem to determine an approximate solution that is optimum. The main goal of this paper is to present new types of proximal contraction for nonself mappings in a fuzzy Banach space. At first, the notion of the best proximity point is presented. We introduce the notion of α ̌–η ̌-β ̌ proximal contractive. After that, the best pr

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47

Karapınar, Erdal. "A Survey on the Fixed Point Theorems via Admissible Mapping." 3C TIC: Cuadernos de desarrollo aplicados a las TIC 11, no. 2 (2022): 26–50. http://dx.doi.org/10.17993/3ctic.2022.112.26-50.

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In this survey, we discuss the crucial role of the notion of admissible mapping in the metric fixed point theory. Adding admissibility conditions to the statements leads not only to generalizing the existing results but also unifying several corresponding results in different settings. In particular, a contraction via admissible mapping involves and covers contractions defined on partially ordered sets, and contractions forming cyclic structure.

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Paul, Mithun, Krishnadhan Sarkar, and Kalishankar Tiwary. "Fixed Point Theorems for Integral-type Weak-Contraction Mappings in Modular Metric Spaces." General Mathematics 31, no. 1 (2023): 21–37. http://dx.doi.org/10.2478/gm-2023-0003.

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Abstract In 2013, Azadifar et al. [3] established fixed point result in integral type contraction in modular metric space and 2020, Chaira et al.[11] established some extensions of Fixed Point Theorems for Weak-Contraction Mapping in Partially Ordered Modular Metric Spaces. In this paper we have established some common fixed point results in integral type contractions in modular and convex modular metric spaces.

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Sabri, Raghad Ibrahaim, and Buthainah Abd Al Hassan Ahmed. "Best Proximity Point Results in Fuzzy Normed Spaces." Science and Technology Indonesia 8, no. 2 (2023): 298–304. http://dx.doi.org/10.26554/sti.2023.8.2.298-304.

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Fixed point (briefly FP ) theory is a potent tool for resolving several actual problems since many problems may be simplified to the FP problem. The idea of Banach contraction mapping is a foundational theorem in FP theory. This idea has wide applications in several fields; hence, it has been developed in numerous ways. Nevertheless, all of these results are reliant on the existence and uniqueness of a FP on some suitable space. Because the FP problem could not have a solution in the case of nonself-mappings, the idea of the best proximity point (briefly Bpp) is offered to approach the best so

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Chen, Chi-Ming, та W. Y. Sun. "Periodic Points and Fixed Points for the Weaker(ϕ,φ)-Contractive Mappings in Complete Generalized Metric Spaces". Journal of Applied Mathematics 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/856974.

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We introduce the notion of weaker(ϕ,φ)-contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.

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