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Journal articles on the topic 'Mathematics. Metric spaces. Mappings (Mathematics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

CHO, Y. J., N. J. HUANG, and L. XIANG. "COINCIDENCE THEOREMS IN COMPLETE METRIC SPACES." Tamkang Journal of Mathematics 30, no. 1 (March 1, 1999): 1–7. http://dx.doi.org/10.5556/j.tkjm.30.1999.4191.

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The purpose of this paper is to introduce new classes of generalized contractive type set-valued mappings and weakly dissipative mappings and to prove some coincidence theorems for these mappings by using the concept of $\omega$-distances.

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2

Zimmerman, Scott. "Sobolev Extensions of Lipschitz Mappings into Metric Spaces." International Mathematics Research Notices 2019, no. 8 (August 21, 2017): 2241–65. http://dx.doi.org/10.1093/imrn/rnx201.

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Abstract Wenger and Young proved that the pair $(\mathbb{R}^m,\mathbb{H}^n)$ has the Lipschitz extension property for $m \leq n$ where $\mathbb{H}^n$ is the sub-Riemannian Heisenberg group. That is, for some $C>0$, any $L$-Lipschitz map from a subset of $\mathbb{R}^m$ into $\mathbb{H}^n$ can be extended to a $CL$-Lipschitz mapping on $\mathbb{R}^m$. In this article, we construct Sobolev extensions of such Lipschitz mappings with no restriction on the dimension $m$. We prove that any Lipschitz mapping from a compact subset of $\mathbb{R}^m$ into $\mathbb{H}^n$ may be extended to a Sobolev mapping on any bounded domain containing the set. More generally, we prove this result in the case of mappings into any Lipschitz $(n-1)$-connected metric space.

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3

Amini, A., M. Fakhar, and J. Zafarani. "KKM mappings in metric spaces." Nonlinear Analysis: Theory, Methods & Applications 60, no. 6 (March 2005): 1045–52. http://dx.doi.org/10.1016/j.na.2004.10.003.

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4

Ćirić, Ljubomir. "On some discontinuous fixed point mappings in convex metric spaces." Czechoslovak Mathematical Journal 43, no. 2 (1993): 319–26. http://dx.doi.org/10.21136/cmj.1993.128397.

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5

Aras, Cigdem Gunduz, Sadi Bayramov, and Murat Ibrahim Yazar. "Soft D-metric spaces." Boletim da Sociedade Paranaense de Matemática 38, no. 7 (October 14, 2019): 137–47. http://dx.doi.org/10.5269/bspm.v38i7.44641.

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6

FUKHAR-UD-DIN, HAFIZ. "Existence and approximation of fixed points in convex metric spaces." Carpathian Journal of Mathematics 30, no. 2 (2014): 175–85. http://dx.doi.org/10.37193/cjm.2014.02.11.

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A fixed point theorem for a generalized nonexpansive mapping is established in a convex metric space introduced by Takahashi [A convexity in metric spaces and nonexpansive mappings, Kodai Math. Sem. Rep., 22 (1970), 142–149]. Our theorem generalizes simultaneously the fixed point theorem of Bose and Laskar [Fixed point theorems for certain class of mappings, Jour. Math. Phy. Sci., 19 (1985), 503–509] and the well-known fixed point theorem of Goebel and Kirk [A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171–174] on a nonlinear domain. The fixed point obtained is approximated by averaging Krasnosel’skii iterations of the mapping. Our results substantially improve and extend several known results in uniformly convex Banach spaces and CAT(0) spaces.

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7

Chernikov, P. V. "Metric spaces and extensions of mappings." Siberian Mathematical Journal 27, no. 6 (1987): 958–62. http://dx.doi.org/10.1007/bf00970017.

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8

Zhou, Qingshan, Yaxiang Li, and Yuehui He. "Quasihyperbolic mappings in length metric spaces." Comptes Rendus. Mathématique 359, no. 3 (April 20, 2021): 237–47. http://dx.doi.org/10.5802/crmath.154.

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9

Bridges, Douglas, and Ray Mines. "Sequentially continuous linear mappings in constructive analysis." Journal of Symbolic Logic 63, no. 2 (June 1998): 579–83. http://dx.doi.org/10.2307/2586851.

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A mapping u: X → Y between metric spaces is sequentially continuous if for each sequence (xn) converging to x ∈ X, (u(xn)) converges to u(x). It is well known in classical mathematics that a sequentially continuous mapping between metric spaces is continuous; but, as all proofs of this result involve the law of excluded middle, there appears to be a constructive distinction between sequential continuity and continuity. Although this distinction is worth exploring in its own right, there is another reason why sequential continuity is interesting to the constructive mathematician: Ishihara [8] has a version of Banach's inverse mapping theorem in functional analysis that involves the sequential continuity, rather than continuity, of the linear mappings; if this result could be upgraded by deleting the word “sequential”, then we could prove constructively the standard versions of the inverse mapping theorem and the closed graph theorem.Troelstra [9] showed that in Brouwer's intuitionistic mathematics (INT) a sequentially continuous mapping on a separable metric space is continuous. On the other hand, Ishihara [6, 7] proved constructively that the continuity of sequentially continuous mappings on a separable metric space is equivalent to a certain boundedness principle for subsets of ℕ; in the same paper, he showed that the latter principle holds within the recursive constructive mathematics (RUSS) of the Markov School. Since it is not known whether that principle holds within Bishop's constructive mathematics (BISH), of which INT and RUSS are models and which can be regarded as the constructive core of mathematics, the exploration of sequential continuity within BISH holds some interest.

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10

Stojakovic, Mila. "Common fixed point theorems in complete metric and probabilistic metric spaces." Bulletin of the Australian Mathematical Society 36, no. 1 (August 1987): 73–88. http://dx.doi.org/10.1017/s0004972700026319.

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In this paper several common fixed point theorems for four continuous mappings in Menger and metric spaces are proved. These mappings are assumed to satisfy some generalizations of the contraction condition.

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11

Khana, Muhammad, Akbar Azam, and Ljubisa Kocinac. "Coincidence of multivalued mappings on metric spaces with a graph." Filomat 31, no. 14 (2017): 4543–54. http://dx.doi.org/10.2298/fil1714543k.

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In this article the coincidence points of a self mapping and a sequence of multivalued mappings are found using the graphic F-contraction. This generalizes Mizoguchi-Takahashi?s fixed point theorem for multivalued mappings on a metric space endowed with a graph. As applications we obtain a theorem in homotopy theory, an existence theorem for the solution of a system of Urysohn integral equations, and for the solution of a special type of fractional integral equations.

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12

Shatanawi, Wasfi, and Kamaleldin Abodayeh. "Some fixed and common fixed point results in G-metric spaces which can't be obtained from metric spaces." Boletim da Sociedade Paranaense de Matemática 38, no. 6 (May 25, 2019): 43–52. http://dx.doi.org/10.5269/bspm.v38i6.40129.

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In this paper, we use the concepts of (A;B)-weakly increasing mappings and altering distance functions to establish new contractive conditions for the pair of mappings in the setting of G-metric spaces. Many Fixed and common Fixed point results in the setting of G{metric spaces are formulated. Note that our new contractive conditions can't be reduces to contractive conditions in standard metric spaces.

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13

Mustafa, Zead, Mona Khandagji, and Wasfi Shatanawi. "Fixed point results on complete G-metric spaces." Studia Scientiarum Mathematicarum Hungarica 48, no. 3 (September 1, 2011): 304–19. http://dx.doi.org/10.1556/sscmath.48.2011.3.1170.

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In this paper several fixed point theorems for a class of mappings defined on a complete G-metric space are proved. In the same time we show that if the G-metric space (X, G) is symmetric then the existence and uniqueness of these fixed point results follows from the Hardy-Rogers theorem in the induced usual metric space (X, dG). We also prove fixed point results for mapping on a G-metric space (X, G) by using the Hardy-Rogers theorem where (X, G) need not be symmetric.

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14

Huang, Xianjiu, Chuanxi Zhu, and Xi Wen. "Common fixed point theorems for families of maps in complete L-fuzzy metric spaces." Filomat 23, no. 3 (2009): 67–80. http://dx.doi.org/10.2298/fil0903067h.

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In this paper, we prove some common fixed point theorems for any even number of compatible mappings in complete L-fuzzy metric spaces. Our main results extend and generalize some known results in fuzzy metric spaces, intuitionistic metric spaces and L-fuzzy metric spaces.

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15

Kadelburg, Zoran, Stojan Radenovic, and Suzana Simic. "Metric spaces and Caristi-Nguyen-type theorems." Filomat 25, no. 3 (2011): 111–24. http://dx.doi.org/10.2298/fil1103111k.

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In this paper we prove cone metric versions of common fixed point theorems for two and four mappings with the Caristi-Nguyen-type contractive conditions. Also, sufficient conditions for two or four mappings to have no common periodic points are deduced. Examples are given to distinguish these results from the known ones and to show that certain conditions cannot be omitted.

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16

Jain, Shobha, Shishir Jain, and Lal Bahadur Jain. "Compatible mappings of type $(\beta)$ and weak compatibility in fuzzy metric spaces." Mathematica Bohemica 134, no. 2 (2009): 151–64. http://dx.doi.org/10.21136/mb.2009.140650.

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17

Priyobarta, N., Bulbul Khomdram, Yumnam Rohen, and Naeem Saleem. "On Generalized Rational α − Geraghty Contraction Mappings in G − Metric Spaces." Journal of Mathematics 2021 (March 9, 2021): 1–12. http://dx.doi.org/10.1155/2021/6661045.

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In this paper, we discuss about various generalizations of α − admissible mappings. Furthermore, we extend the concept of α − admissible to generalize rational α − Geraghty contraction in G − metric space. With this new contraction mapping, we establish some fixed-point theorems in G − metric space. The obtained result is verified with an example.

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18

Wisniewski, Andrzej. "The Structure of Measurable Mappings on Metric Spaces." Proceedings of the American Mathematical Society 122, no. 1 (September 1994): 147. http://dx.doi.org/10.2307/2160853.

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19

Khamsi, M. A. "On asymptotically nonexpansive mappings in hyperconvex metric spaces." Proceedings of the American Mathematical Society 132, no. 2 (August 28, 2003): 365–73. http://dx.doi.org/10.1090/s0002-9939-03-07172-7.

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20

Wiśniewski, Andrzej. "The structure of measurable mappings on metric spaces." Proceedings of the American Mathematical Society 122, no. 1 (January 1, 1994): 147. http://dx.doi.org/10.1090/s0002-9939-1994-1201807-0.

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21

Tiammee, Jukrapong, and Suthep Suantai. "Endpoints of multi-valued weakly contraction in complete metric spaces endowed with graphs." Filomat 31, no. 14 (2017): 4319–29. http://dx.doi.org/10.2298/fil1714319t.

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In this paper, we introduce a new concept of weak G-contraction for multi-valued mappings on a metric space endowed with a directed graph. Endpoint theorem of this mapping is established under some sufficient conditions in a complete metric space endowed with a directed graph. Our main results extend and generalize those fixed point in partially ordered metric spaces. Some examples supporting our main results are also given. Moreover, we apply our main results to obtain some coupled fixed point results in the context of complete metric spaces endowed with a directed graph which are more general than those in partially ordered metric spaces.

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22

KAEWKHAO, A., C. KLANGPRAPHAN, and B. PANYANAK. "Fixed points of Osilike-Berinde-G-nonexpansive mappings in metric spaces endowed with graphs." Carpathian Journal of Mathematics 37, no. 2 (June 9, 2021): 311–23. http://dx.doi.org/10.37193/cjm.2021.02.16.

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"In this paper, we introduce the notion of Osilike-Berinde-G-nonexpansive mappings in metric spaces and show that every Osilike-Berinde-G-nonexpansive mapping with nonempty fixed point set is a G-quasinonexpansive mapping. We also prove the demiclosed principle and apply it to obtain a fixed point theorem for Osilike-Berinde-G-nonexpansive mappings. Strong and \Delta-convergence theorems of the Ishikawa iteration process for G-quasinonexpansive mappings are also discussed."

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23

Kutbi, Marwan Amin, Jamshaid Ahmad, and Akbar Azam. "On Fixed Points ofα-ψ-Contractive Multivalued Mappings in Cone Metric Spaces." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/313782.

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We define the notion ofα*-ψ-contractive mappings for cone metric space and obtain fixed points of multivalued mappings in connection with Hausdorff distance function for closed bounded subsets of cone metric spaces. We obtain some recent results of the literature as corollaries of our main theorem. Moreover, a nontrivial example ofα*-ψ-contractive mapping satisfying all conditions of our main result has been constructed.

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24

Klin-eam, Chakkrid, and Cholatis Suanoom. "Some Common Fixed-Point Theorems for Generalized-Contractive-Type Mappings on Complex-Valued Metric Spaces." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/604215.

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Fixed-point theory in complex valued metric spaces has greatly developed in recent times. In this paper, we prove certain common fixed-point theorems for two single-valued mappings in such spaces. The mappings we consider here are assumed to satisfy certain metric inequalities with generalized fixed-point theorems due to Rouzkard and Imdad (2012). This extends and subsumes many results of other authors which were obtained for mappings on complex-valued metric spaces.

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25

Basha, S. Sadiq, N. Shahzad, and R. Jeyaraj. "Optimal Approximate Solutions of Fixed Point Equations." Abstract and Applied Analysis 2011 (2011): 1–9. http://dx.doi.org/10.1155/2011/174560.

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The main objective of this paper is to present some best proximity point theorems for K-cyclic mappings and C-cyclic mappings in the frameworks of metric spaces and uniformly convex Banach spaces, thereby furnishing an optimal approximate solution to the equations of the form where is a non-self mapping.

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26

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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27

Manro, Saurabh, Sanjay Kumar, S. S. Bhatia, and Kenan Tas. "Common Fixed Point Theorems in Modified Intuitionistic Fuzzy Metric Spaces." Journal of Applied Mathematics 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/189321.

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This paper consists of main two sections. In the first section, we prove a common fixed point theorem in modified intuitionistic fuzzy metric space by combining the ideas of pointwiseR-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions. In the second section, we prove common fixed point theorems in modified intuitionistic fuzzy metric space from the class of compatible continuous mappings to noncompatible and discontinuous mappings. Lastly, as an application, we prove fixed point theorems using weakly reciprocally continuous noncompatible self-mappings on modified intuitionistic fuzzy metric space satisfying some implicit relations.

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28

Vetro, Francesca. "Fixed point results for nonexpansive mappings on metric spaces." Filomat 29, no. 9 (2015): 2011–20. http://dx.doi.org/10.2298/fil1509011v.

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In this paper we obtain some fixed point results for a class of nonexpansive single-valued mappings and a class of nonexpansive multi-valued mappings in the setting of a metric space. The contraction mappings in Banach sense belong to the class of nonexpansive single-valued mappings considered herein. These results are generalizations of the analogous ones in Khojasteh et al. [Abstr. Appl. Anal. 2014 (2014), Article ID 325840].

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29

Kumam, Poom, Calogero Vetro, and Francesca Vetro. "Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/986028.

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Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

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30

Ninsri, Aphinat, and Wutiphol Sintunavarat. "Approximation fixed theorems for α-partial weakly Zamfirescu mappings with application to homotopy invariance." Filomat 30, no. 7 (2016): 1941–56. http://dx.doi.org/10.2298/fil1607941n.

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In this paper, we introduce the concept of ?-partial weakly Zamfirescu mappings and give some approximate fixed point results for this mapping in ?-complete metric spaces. We also give some approximate fixed point results in ?-complete metric space endowed with an arbitrary binary relation and approximate fixed point results in ?-complete metric space endowed with graph. As application, we give homotopy results for ?-partial weakly Zamfirescu mapping.

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31

Beraz, Ashis, Hiranmoy Garai, Bosko Damjanovic, and Ankush Chanda. "Some interesting results on F-metric spaces." Filomat 33, no. 10 (2019): 3257–68. http://dx.doi.org/10.2298/fil1910257b.

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In this manuscript, we prove that the newly introduced F-metric spaces are Hausdorff and first countable. We investigate some interrelations among the Lindel?fness, separability and second countability axiom in the setting of F-metric spaces. Moreover, we acquire some interesting fixed point results concerning altering distance functions for contractive type mappings and Kannan type contractive mappings in this exciting context. In addition, most of the findings are well-furnished by several non-trivial examples. Finally, we raise an open problem regarding the structure of an open set in this setting.

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32

Babu, G. V. R., and G. N. Alemayehu. "Fixed points of nodal contractions in cone metric spaces." Tamkang Journal of Mathematics 42, no. 1 (March 22, 2011): 39–51. http://dx.doi.org/10.5556/j.tkjm.42.2011.595.

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We introduce local power contractions and nodal contractions in cone metric spaces and prove the existence of fixed points of such contractions in cone metric spaces. Our theorems generalize the results of Haung and Zhang [L-G. Haung, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476].

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33

Salimi, Peyman, Calogero Vetro, and Pasquale Vetro. "Some new fixed point results in non-Archimedean fuzzy metric spaces." Nonlinear Analysis: Modelling and Control 18, no. 3 (July 25, 2013): 344–58. http://dx.doi.org/10.15388/na.18.3.14014.

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In this paper, we introduce the notions of fuzzy (α,β,ϕ)-contractive mapping, fuzzy α-φ-ψ-contractive mapping and fuzzy α-β-contractive mapping and establish some results of fixed point for this class of mappings in the setting of non-Archimedean fuzzy metric spaces. The results presented in this paper generalize and extend some recent results in fuzzy metric spaces. Also, some examples are given to support the usability of our results.

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34

KHAMSI, M. A., and A. R. KHAN. "Goebel and Kirk fixed point theorem for multivalued asymptotically nonexpansive mappings." Carpathian Journal of Mathematics 33, no. 3 (2017): 335–42. http://dx.doi.org/10.37193/cjm.2017.03.08.

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We introduce the concept of a multivalued asymptotically nonexpansive mapping and establish Goebel and Kirk fixed point theorem for these mappings in uniformly hyperbolic metric spaces. We also define a modified Mann iteration process for this class of mappings and obtain an extension of some well-known results for singlevalued mappings defined on linear as well as nonlinear domains.

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35

Gabeleh, Moosa, Olivier Otafudu, and Naseer Shahzad. "Coincidence best proximity points in convex metric spaces." Filomat 32, no. 7 (2018): 2451–63. http://dx.doi.org/10.2298/fil1807451g.

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Let T,S : A U B ? A U B be mappings such that T(A) ? B,T(B)? A and S(A) ? A,S(B)?B. Then the pair (T,S) of mappings defined on A[B is called cyclic-noncyclic pair, where A and B are two nonempty subsets of a metric space (X,d). A coincidence best proximity point p ? A U B for such a pair of mappings (T,S) is a point such that d(Sp,Tp) = dist(A,B). In this paper, we study the existence and convergence of coincidence best proximity points in the setting of convex metric spaces. We also present an application of one of our results to an integral equation.

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36

BORCUT, MARIN. "Tripled coincidence theorems for monotone mappings in partially ordered metric spaces." Creative Mathematics and Informatics 21, no. 2 (2012): 135–42. http://dx.doi.org/10.37193/cmi.2012.02.15.

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In this paper, we establish tripled coincidence point theorems for a pair of mappings F : X × X × X → X and g : X → X satisfying a nonlinear contractive condition ordered metric spaces. Presented theorems extend several existing results in the literature: [Borcut, M. and Berinde, V., Tripled coincidente point theorems for contractive type mappings in partially ordered metric spaces, Aplied Mathematics and Computation, 218 (2012), No. 10, 5929–5936], and Berinde, Borcut in article [Berinde, V., Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 4889-4897].

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37

Fakhar, M., F. Mirdamadi, and Z. Soltani. "Some results on best proximity points of cyclic Meir-Keeler contraction mappings." Filomat 32, no. 6 (2018): 2081–89. http://dx.doi.org/10.2298/fil1806081f.

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In this paper, we study the existence and uniqueness of best proximity points for cyclic Meir-Keeler contraction mappings in metric spaces with the property W-WUC. Also, the existence of best proximity points for set-valued cyclic Meir-Keeler contraction mappings in metric spaces with the property WUC are obtained

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38

Gaba, Yaé Ulrich, Maggie Aphane, and Hassen Aydi. "α , BK -Contractions in Bipolar Metric Spaces." Journal of Mathematics 2021 (February 26, 2021): 1–6. http://dx.doi.org/10.1155/2021/5562651.

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39

Huang, Xiaojun, Hongjun Liu, and Jinsong Liu. "Local properties of quasihyperbolic mappings in metric spaces." Annales Academiae Scientiarum Fennicae Mathematica 41 (February 2016): 23–40. http://dx.doi.org/10.5186/aasfm.2016.4106.

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40

Arutyunov, A. V. "Covering mappings in metric spaces and fixed points." Doklady Mathematics 76, no. 2 (October 2007): 665–68. http://dx.doi.org/10.1134/s1064562407050079.

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41

Davydov, N. A. "Properties of continuous mappings of unbounded metric spaces." Ukrainian Mathematical Journal 43, no. 4 (April 1991): 388–91. http://dx.doi.org/10.1007/bf01670082.

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42

Davydov, N. A. "Properties of continuous mappings of unbounded metric spaces." Ukrainian Mathematical Journal 43, no. 3 (March 1991): 388–91. http://dx.doi.org/10.1007/bf01060852.

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43

Sevost’yanov, E. A., S. O. Skvortsov, and E. A. Petrov. "On Equicontinuous Families of Mappings of Metric Spaces." Ukrainian Mathematical Journal 72, no. 10 (March 2021): 1634–49. http://dx.doi.org/10.1007/s11253-021-01877-3.

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44

Gabeleh, Moosa, and Naseer Shahzad. "Best proximity pair and fixed point results for noncyclic mappings in convex metric spaces." Filomat 30, no. 12 (2016): 3149–58. http://dx.doi.org/10.2298/fil1612149g.

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In this article, we formulate a best proximity pair theorem for noncyclic relatively nonexpansive mappings in convex metrc spaces by using a geometric notion of semi-normal structure. In this way, we generalize a corresponding result in [W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai Math. Sem. Rep. 22 (1970) 142-149]. We also establish a best proximity pair theorem for pointwise noncyclic contractions in the setting of convex metric spaces. Our result generalizes a result due to Sankara Raju Kosuru and Veeramani [G. Sankara Raju Kosuru and P. Veeramani, A note on existence and convergence of best proximity points for pointwise cyclic contractions, Numer. Funct. Anal. Optim., 82 (2011) 821-830].

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45

Heng, Weng-Seng, Wei-Shih Du, and Chi-Lin Yen. "New Existence Results for Fixed Point Problem and Minimization Problem in Compact Metric Spaces." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/635903.

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We first present some new existence theorems for fixed point problem and minimization problem in compact metric spaces without assuming that mappings possess convexity property. Some applications of our results to new fixed point theorems for nonself mappings in the setting of strictly convex normed linear spaces and usual metric spaces are also given.

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46

Alsamir, Habes, Mohd Noorani, Wasfi Shatanawi, and Kamal Abodyah. "Common fixed point results for generalized (ψ,β)-geraghty contraction type mapping in partially ordered metric-like spaces with application." Filomat 31, no. 17 (2017): 5497–509. http://dx.doi.org/10.2298/fil1717497a.

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Harandi [A. A. Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages] introduced the notion of metric-like spaces as a generalization of partial metric spaces and studied some fixed point theorems in the context of the metric-like spaces. In this paper, we utilize the notion of the metric-like spaces to introduce and prove some common fixed points theorems for mappings satisfying nonlinear contractive conditions in partially ordered metric-like spaces. Also, we introduce an example and an application to support our work. Our results extend and modify some recent results in the literature.

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47

Popa, Valeriu, and Dan Popa. "Fixed point theorems of generalized Gregus type in quasi-metric spaces for two pairs of mappings satisfying common coincidence range property." Filomat 34, no. 11 (2020): 3561–66. http://dx.doi.org/10.2298/fil2011561p.

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The purpose of this paper is to prove some general fixed point theorems for two pairs of mappings satisfying implicit relations of generalized Gregus type in quasi-metric spaces without the notion of sequence and inequality. As applications we obtain new results for mappings satisfying contractive / extensive conditions of integral type and in G-metric spaces.

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48

Mahmoud, Sid, Muneo ChO, and Ji Lee. "(m,q)-isometric and (m,∞)-isometric tuples of commutative mappings on a metric space." Filomat 34, no. 7 (2020): 2425–37. http://dx.doi.org/10.2298/fil2007425m.

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In this paper, we introduce new concepts of (m,q)-isometries and (m,?)-isometries tuples of commutative mappings on metrics spaces. We discuss the most interesting results concerning this class of mappings obtained form the idea of generalizing the (m,q)-isometries and (m,?)-isometries for single mappings. In particular, we prove that if T = (T1,..., Tn) is an (m,q)-isometric commutative and power bounded tuple, then T is a (1,q)-isometric tuple. Moreover, we show that if T = (T1,...,Td) is an (m,?)- isometric commutative tuple of mappings on a metric space (E,d), then there exists a metric d? on E such that T is a (1,?)-isometric tuple on (E,d?).

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49

SAKSIRIKUN, WARUT, and NARIN PETROT. "Some fixed point theorems via partial order relations without the monotone property." Carpathian Journal of Mathematics 31, no. 3 (2015): 389–94. http://dx.doi.org/10.37193/cjm.2015.03.16.

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The main aim of this paper is to consider some fixed point theorems via a partial order relation in complete metric spaces, when the considered mapping may not satisfy the monotonic properties. Furthermore, we also obtain some couple fixed point theorems, which can be viewed as an extension of a result that was presented in [V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 7347–7355].

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50

Dobrowolski, T. "On extending mappings into nonlocally convex linear metric spaces." Proceedings of the American Mathematical Society 93, no. 3 (March 1, 1985): 555. http://dx.doi.org/10.1090/s0002-9939-1985-0774022-7.

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