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Journal articles on the topic 'Nonlinear contraction'

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Published: 5 June 2025

Last updated: 2 August 2025

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1

BARREIRA, LUIS, and CLAUDIA VALLS. "Stability of L1 contractions." Mathematical Proceedings of the Cambridge Philosophical Society 159, no. 1 (2015): 23–46. http://dx.doi.org/10.1017/s0305004115000158.

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AbstractThe notion of an exponential contraction is only one among many possible rates of contraction of a nonautonomous system, while for an autonomous system all contractions are exponential. We consider the notion of an L1 contraction that includes exponential contractions as a very particular case and that is naturally adapted to the variation-of-parameters formula. Both for discrete and continuous time, we show that under very general assumptions the notion of an L1 contraction persists under sufficiently small linear and nonlinear perturbations, also maintaining the type of stability. As

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2

Arif, Mohammad, and Mohammad Imdad. "Fixed point results under nonlinear Suzuki (F,R≠)-contractions with an application." Filomat 36, no. 9 (2022): 3155–65. http://dx.doi.org/10.2298/fil2209155a.

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In this article, we introduce the idea of nonlinear Suzuki (F,R?)-contractions, which is patterned after the contractive conditions due to Suzuki [Nonlinear Anal. 71 (2009) 5313-5317] and Wardowski [Fixed Point Theory Appl. (2012) 94:6]. Utilizing our newly introduced contraction, we establish some relation theoretic fixed point theorems. Furthermore, we adopt an example to highlight the genuineness of our newly proved results. Finally, we use our main results to establish the existence and uniqueness of solution for a nonlinear matrix equation.

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3

Jha, Pavan Kumar. "Contraction Principles in Metric Space." NUTA Journal 11, no. 1-2 (2024): 39–44. https://doi.org/10.3126/nutaj.v11i1-2.77020.

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This paper deals with contractions in metric. some historical accounts on contractions principles in metric space. Banach Contraction Principle is marvelous and widely applied fixed point theorem in nonlinear analysis. every contraction in a complete metric space has a unique fixed point.

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4

Saugen, E., and N. K. Vollestad. "Nonlinear relationship between heat production and force during voluntary contractions in humans." Journal of Applied Physiology 79, no. 6 (1995): 2043–49. http://dx.doi.org/10.1152/jappl.1995.79.6.2043.

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The rate of temperature rise (dT/dt) in the vastus lateralis muscle of seven subjects was measured at four to five locations in each muscle during voluntary isometric contractions ranging from 10 to 90% of maximal voluntary contraction (MVC) force. dT/dt increased from 3.1 +/- 1.1 mK/s at 10% MVC to 14.5 +/- 1.3 mK/s at 90% MVC. In the typical subject, the increase in dT/dt with force was markedly higher between 30 and 70% MVC than in the upper and lower force ranges. The estimated ratio between heat rate in active muscle and force was six times higher at 10% MVC than at 90% MVC, indicating a

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5

Lo'Lo', Parvaneh, Maryam Shams, and Manuel De la Sen. "Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space." Nonlinear Analysis: Modelling and Control 28 (April 26, 2023): 1–19. http://dx.doi.org/10.15388/namc.2023.28.32119.

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In a recent paper, Khojasteh et al. presented a new collection of simulation functions, said Z-contraction. This form of contraction generalizes the Banach contraction and makes different types of nonlinear contractions. In this article, we discuss a pair of nonlinear operators that applies to a nonlinear contraction including a simulation function in a partially ordered metric space. For this pair of operators with and without continuity, we derive some results about the coincidence and unique common fixed point. In the following, many known and dependent consequences in fixed point theory in

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Gholidahneh, Abdolsattar, Shaban Sedghi, and Vahid Parvaneh. "Some Fixed Point Results for Perov-Ćirić-Prešić Type F-Contractions with Application." Journal of Function Spaces 2020 (August 28, 2020): 1–9. http://dx.doi.org/10.1155/2020/1464125.

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Ćirić and Prešić developed the concept of Prešić contraction to Ćirić-Prešić type contractive mappings in the background of a metric space. On the other hand, Altun and Olgun introduced Perov type F-contractions. In this paper, we extend the concept of Ćirić-Prešić contractions to Perov-Ćirić-Prešić type F-contractions. Our results modify some known ones in the literature. To support our main result, an example and an application to nonlinear operator systems are presented.

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Moussaoui, Abdelhamid, Said Melliani, and Stojan Radenovic. "A nonlinear fuzzy contraction principle via control functions." Filomat 38, no. 6 (2024): 1963–72. http://dx.doi.org/10.2298/fil2406963m.

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In this work, we develop a new type of nonlinear fuzzy contraction, namely fuzzy L?-weak contraction, based on fuzzy L?-simulation function and fuzzy ?f-contractive mappings. Then, using the specifically developed contraction, we show the existence and uniqueness of a fixed point for a self-mapping in complete fuzzy metric spaces. We provide an example, together with some illustrative corollaries and remarks, to further prove the validity of our findings. The presented findings combine, enhance, and extend a number of earlier research findings.

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8

Liao, Fang-fang, Yongxin Jiang, and Zhiting Xie. "A Generalized Nonuniform Contraction and Lyapunov Function." Abstract and Applied Analysis 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/613038.

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For nonautonomous linear equationsx′=A(t)x, we give a complete characterization of general nonuniform contractions in terms of Lyapunov functions. We consider the general case of nonuniform contractions, which corresponds to the existence of what we call nonuniform(D,μ)-contractions. As an application, we establish the robustness of the nonuniform contraction under sufficiently small linear perturbations. Moreover, we show that the stability of a nonuniform contraction persists under sufficiently small nonlinear perturbations.

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Nisar, Zubair, Nayyar Mehmood, Akbar Azam, Faryad Ali та Mohammed A. Al-Kadhi. "Exploring Integral Ϝ-Contractions with Applications to Integral Equations and Fractional BVPs". Fractal and Fractional 7, № 12 (2023): 833. http://dx.doi.org/10.3390/fractalfract7120833.

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In this article, two types of contractive conditions are introduced, namely extended integral Ϝ-contraction and (ϰ,Ω-Ϝ)-contraction. For the case of two mappings and their coincidence point theorems, a variant of (ϰ,Ω-Ϝ)-contraction has been introduced, which is called (ϰ,Γ1,2,Ω-Ϝ)-contraction. In the end, the applications of an extended integral Ϝ-contraction and (ϰ,Ω-Ϝ)-contraction are given by providing an existence result in the solution of a fractional order multi-point boundary value problem involving the Riemann–Liouville fractional derivative. An interesting existence result for the so

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10

Karapınar, Erdal, and Andreea Fulga. "An admissible Hybrid contraction with an Ulam type stability." Demonstratio Mathematica 52, no. 1 (2019): 428–36. http://dx.doi.org/10.1515/dema-2019-0037.

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AbstractIn this manuscript, we introduce a new hybrid contraction that unify several nonlinear and linear contractions in the set-up of a complete metric space. We present an example to indicate the genuine of the proved result. In addition, we consider Ulam type stability and well-posedness for this new hybrid contraction.

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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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Zakany, Monica. "Multivalued self almost local contractions." Annals of West University of Timisoara - Mathematics and Computer Science 57, no. 1 (2019): 122–38. http://dx.doi.org/10.2478/awutm-2019-0010.

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Abstract We introduce a new class of contractive mappings: the almost local contractions, starting from the almost contractions presented by V. Berinde in [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration Nonlinear Analysis Forum 9 (2004) No.1, 43-53], and also from the concept of local contraction presented by Filipe Martins da Rocha and Vailakis in [V. Filipe Martins-da-Rocha, Y. Vailakis, Existence and uniqueness of a fixed point for local contractions, Econometrica, vol.78, No.3 (May, 2010) 1127-1141]. First of all, we present the notion of multivalued

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CLARKE, S. R., and R. H. J. GRIMSHAW. "Weakly nonlinear internal wave fronts trapped in contractions." Journal of Fluid Mechanics 415 (July 25, 2000): 323–45. http://dx.doi.org/10.1017/s0022112000008715.

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The propagation of weakly nonlinear, long internal wave fronts in a contraction is considered in the transcritical limit as a model for the establishment of virtual controls. It is argued that the appropriate equation to describe this process is a variable coefficient Korteweg–de Vries equation. The solutions of this equation are then considered for compressive and rarefaction fronts. Rarefaction fronts exhibit both normal and virtual control solutions. However, the interaction of compressive fronts with contractions is intrinsically unsteady. Here the dynamics take two forms, interactions wit

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Dhawan, Pooja, Kapil Jain та Jatinderdeep Kaur. "αH-ψH-Multivalued Contractive Mappings and Related Results in Complete Metric Spaces with An Application". Mathematics 7, № 1 (2019): 68. http://dx.doi.org/10.3390/math7010068.

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In the present article, the notion of αH-ψH-multivalued contractive type mappings is introduced and some fixed point results in complete metric spaces are studied. These theorems generalize Nadler’s (Multivalued contraction mappings, Pac. J. Math., 30, 475–488, 1969) and Suzuki-Kikkawa's (Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69, 2942–2949, 2008) results that exist in the literature. The effectiveness of the obtained results has been verified with the help of some comparative examples. Moreover, a homotopy result has

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15

Din, Muhammad, Umar Ishtiaq, Muzammil Mukhtar, Salvatore Sessa, and Hassan Ali Ghazwani. "On Generalized Sehgal–Guseman-Like Contractions and Their Fixed-Point Results with Applications to Nonlinear Fractional Differential Equations and Boundary Value Problems for Homogeneous Transverse Bars." Mathematics 12, no. 4 (2024): 541. http://dx.doi.org/10.3390/math12040541.

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The goal of this study is to describe the class of modified Sehgal–Guseman-like contraction mappings and set up some fixed-point results in S-metric spaces. The class of generalized Sehgal–Guseman-like contraction mappings contains enhancements of Banach contractions, Kannan contractions, Chatterjee contractions, Chatterjee-type contractions, quasi-contractions, Ćirić–Reich–Rus-type contractions, Hardy–Rogers-type contractions, Reich-type contractions, interpolative Kannan contractions, interpolative Chatterjee contractions, among others, with their generalizations in S-metric spaces. We offer

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16

Pant, Rajendra. "Fixed point theorems for nonlinear contractions with applications to iterated function systems." Applied General Topology 19, no. 1 (2018): 163. http://dx.doi.org/10.4995/agt.2018.7918.

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We introduce a new type of nonlinear contraction and present some fixed point results without using continuity or semi-continuity. Our result complement, extend and generalize a number of fixed point theorems including the the well-known Boyd and Wong theorem [On nonlinear contractions, Proc. Amer. Math. Soc. 20(1969)]. Also we discuss an application to iterated function systems.

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17

Alqahtani, Aydi, Karapınar, and Rakočević. "A Solution for Volterra Fractional Integral Equations by Hybrid Contractions." Mathematics 7, no. 8 (2019): 694. http://dx.doi.org/10.3390/math7080694.

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In this manuscript, we propose a solution for Volterra type fractional integral equations by using a hybrid type contraction that unifies both nonlinear and linear type inequalities in the context of metric spaces. Besides this main goal, we also aim to combine and merge several existing fixed point theorems that were formulated by linear and nonlinear contractions.

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18

Abodayeh, Kamaleldin, Erdal Karapınar, Ariana Pitea, and Wasfi Shatanawi. "Hybrid Contractions on Branciari Type Distance Spaces." Mathematics 7, no. 10 (2019): 994. http://dx.doi.org/10.3390/math7100994.

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In this manuscript, we consider some hybrid contractions that merge linear and nonlinear contractions in the abstract spaces induced by the Branciari distance and the Branciari b-distance. More precisely, we introduce the notion of a ( p , c ) -weight type ψ -contraction in the setting of Branciari distance spaces and the concept of a ( p , c ) -weight type contraction in Branciari b-distance spaces. We investigate the existence of a fixed point of such operators in Branciari type distance spaces and illustrate some examples to show that the presented results are genuine in the literature.

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19

Sitthiwirattham, Thanin, Jessada Tariboon, and Sotiris K. Ntouyas. "Three-Point Boundary Value Problems of Nonlinear Second-Orderq-Difference Equations Involving Different Numbers ofq." Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/763786.

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We study a new class of three-point boundary value problems of nonlinear second-orderq-difference equations. Our problems contain different numbers ofqin derivatives and integrals. By using a variety of fixed point theorems (such as Banach’s contraction principle, Boyd and Wong fixed point theorem for nonlinear contractions, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative) and Leray-Schauder degree theory, some new existence and uniqueness results are obtained. Illustrative examples are also presented.

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20

Sahin, Hakan. "A New Best Proximity Point Result with an Application to Nonlinear Fredholm Integral Equations." Mathematics 10, no. 4 (2022): 665. http://dx.doi.org/10.3390/math10040665.

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In the current paper, we first introduce a new class of contractions via a new notion called p-cyclic contraction mapping by combining the ideas of cyclic contraction mapping and p-contraction mapping. Then, we give a new definition of a cyclically 0-complete pair to weaken the completeness condition on the partial metric spaces. Following that, we prove some best proximity point results for p-cyclic contraction mappings on D∪E where D,E is a cyclically 0-complete pair in the setting of partial metric spaces. Hence, we generalize and unify famous and well-known results in the literature of met

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21

Siegle, M. L., S. Buhner, M. Schemann, H. R. Schmid, and H. J. Ehrlein. "Propagation velocities and frequencies of contractions along canine small intestine." American Journal of Physiology-Gastrointestinal and Liver Physiology 258, no. 5 (1990): G738—G744. http://dx.doi.org/10.1152/ajpgi.1990.258.5.g738.

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This study was performed to clarify in detail the behavior of the propagation velocities and frequencies of contractions along the canine small intestine. In conscious dogs, duodenal, jejunal, and ileal contractions were recorded by multiple, closely spaced strain gauges and analyzed by a computerized method. During both the interdigestive and postprandial states, the propagation velocity increased from the duodenal bulb to the distal duodenum and declined aborally within the jejunum, reaching rather constant values in the ileum. The decrease was steepest in the proximal part of the jejunum. I

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22

Abdou, Afrah Ahmad Noman. "Solving a Nonlinear Fractional Differential Equation Using Fixed Point Results in Orthogonal Metric Spaces." Fractal and Fractional 7, no. 11 (2023): 817. http://dx.doi.org/10.3390/fractalfract7110817.

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This research article aims to solve a nonlinear fractional differential equation by fixed point theorems in orthogonal metric spaces. To achieve our goal, we define an orthogonal Θ-contraction and orthogonal (α,Θ)-contraction in the setting of complete orthogonal metric spaces and prove fixed point theorems for such contractions. In this way, we consolidate and amend innumerable celebrated results in fixed point theory. We provide a non-trivial example to show the legitimacy of the established results.

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23

Ćirić, Ljubomir. "Multi-valued nonlinear contraction mappings." Nonlinear Analysis: Theory, Methods & Applications 71, no. 7-8 (2009): 2716–23. http://dx.doi.org/10.1016/j.na.2009.01.116.

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24

Babacev, Natasa. "Nonlinear generalized contractions on Menger PM spaces." Applicable Analysis and Discrete Mathematics 6, no. 2 (2012): 257–64. http://dx.doi.org/10.2298/aadm120526012b.

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This paper presents a fixed point theorem for a self-mapping defined on probabilistic Menger spaces satisfying nonlinear generalized contractive type conditions. The theorem is an improvement of a result presented by B.S. Choudhury, K. Das: A new contraction principle in Menger spaces, Acta Mathematica Sinica 24 (2008), 1379{1386. This is illustrated with an example.

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Mudhesh, Mustafa, Aftab Hussain, Muhammad Arshad, and Hamed Alsulami. "A Contemporary Approach of Integral Khan-Type Multivalued Contractions with Generalized Dynamic Process and an Application." Mathematics 11, no. 20 (2023): 4318. http://dx.doi.org/10.3390/math11204318.

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The aim of this article is to investigate the relationship between integral-type contractions and the generalized dynamic process. The fixed-point results for multivalued mappings that satisfy both the integral Khan-type contraction and the integral θ-contraction are established in a complete metric space. Furthermore, some corollaries are derived based on our main contribution. To demonstrate the novelty of our findings, several examples are provided. Finally, we look into whether nonlinear fractional differential equations have solutions utilizing the obtained results.

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WEIMAR-WOODS, EVELYN. "THE GENERAL STRUCTURE OF G-GRADED CONTRACTIONS OF LIE ALGEBRAS, II: THE CONTRACTED LIE ALGEBRA." Reviews in Mathematical Physics 18, no. 06 (2006): 655–711. http://dx.doi.org/10.1142/s0129055x06002760.

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We continue our study of G-graded contractions γ of Lie algebras where G is an arbitrary finite Abelian group. We compare them with contractions, especially with respect to their usefulness in physics. (Note that the unfortunate terminology "graded contraction" is confusing since they are, by definition, not contractions.)We give a complete characterization of continuous G-graded contractions and note that they are equivalent to a proper subset of contractions. We study how the structure of the contracted Lie algebra Lγdepends on γ, and show that, for discrete graded contractions, applications

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Jesic, Sinisa, Natasa Cirovic, and Donal O’Regan. "Altering distances and a common fixed point theorem in Menger probabilistic metric spaces." Filomat 31, no. 2 (2017): 175–81. http://dx.doi.org/10.2298/fil1702175j.

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This paper presents a common fixed point theorem for two compatible self-mappings satisfying nonlinear contractive type condition defined using a ?-function. This result extends previous results due to B. S. Choudhury, K. Das, A new contraction principle in Menger spaces, Acta Mathematica Sinica 24 (2008) 1379-1386, and the result due to D. Mihe?, Altering distances in probabilistic Menger spaces, Nonlinear Analysis 71 (2009) 2734-2738.

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Clarke, S. R., and R. H. J. Grimshaw. "Resonantly generated internal waves in a contraction." Journal of Fluid Mechanics 274 (September 10, 1994): 139–61. http://dx.doi.org/10.1017/s0022112094002077.

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The near-resonant flow of a stratified fluid through a localized contraction is considered in the long-wavelength weakly nonlinear limit to investigate the transient development of nonlinear internal waves and whether these might lead to local steady hydraulic flows. It is shown that under these circumstances the response of the fluid will fall into one of three categories, the first governed by a forced Korteweg–de Vries equation and the latter two by a variable-coefficient form of this equation. The variable-coefficient equation is discussed using analytical approximations and numerical solu

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Thuý, Đặng Lệ, Cao Thanh Tinh, Lê Trung Hiếu, and Lê Huỳnh Mỹ Vân. "New sufficient criteria for epsilon-contraction of a class of nonlinear diference system with continuous time." Science and Technology Development Journal - Natural Sciences 3, no. 3 (2020): 213–24. http://dx.doi.org/10.32508/stdjns.v3i3.649.

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Contraction property of dynamical systems, especially difference systems, is one of the qualitative properties which have attracted much attention from many researchers for recent decades. Contraction of dynamical systems has many practical applications which means that two trajectories of the system convergence to each other when the time reaches to positive infinity. In this paper, by improving some existing approaches, we present a new approach to contraction problem of a class of nonlinear time-varying delay difference system with continuous time. We generalize the definition of contractio

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Livingston, J. Z., J. R. Resar, and F. C. Yin. "Effect of tetanic myocardial contraction on coronary pressure-flow relationships." American Journal of Physiology-Heart and Circulatory Physiology 265, no. 4 (1993): H1215—H1226. http://dx.doi.org/10.1152/ajpheart.1993.265.4.h1215.

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Cardiac contraction causes a decrease in coronary flow. Despite many studies, it is still not clear what mechanism or mechanisms are responsible for this flow decrease. The phasic nature of myocardial contraction and the complexities intrinsic to intact heart preparations make it difficult to elucidate the mechanisms. We therefore studied coronary pressure-flow relationships during steady-state (tetanic) contractions in the maximally vasodilated isolated canine interventricular septum to see whether waterfall-type behavior is present. Using ryanodine and electrical stimulation allowed the prod

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Mohamadi, M., R. Saadati, A. Shahmari, and S. M. Vaezpour. "Nonlinear Contraction Theorems in Fuzzy Spaces." Journal of Applied Sciences 9, no. 7 (2009): 1397–400. http://dx.doi.org/10.3923/jas.2009.1397.1400.

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Lopez, Brett T., and Jean-Jacques E. Slotine. "Adaptive Nonlinear Control With Contraction Metrics." IEEE Control Systems Letters 5, no. 1 (2021): 205–10. http://dx.doi.org/10.1109/lcsys.2020.3000190.

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Nguyen, Hung D., Thanh Long Vu, Jean-Jacques Slotine, and Konstantin Turitsyn. "Contraction Analysis of Nonlinear DAE Systems." IEEE Transactions on Automatic Control 66, no. 1 (2021): 429–36. http://dx.doi.org/10.1109/tac.2020.2981348.

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O’Regan, Donal, and Reza Saadati. "Nonlinear contraction theorems in probabilistic spaces." Applied Mathematics and Computation 195, no. 1 (2008): 86–93. http://dx.doi.org/10.1016/j.amc.2007.04.070.

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Lohmiller, Winfried, and Jean-Jacques E. Slotine. "Nonlinear process control using contraction theory." AIChE Journal 46, no. 3 (2000): 588–96. http://dx.doi.org/10.1002/aic.690460317.

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Pérez, A. Flores, Yu Tang, and Ileana Grave. "Contraction based identification for nonlinear systems." IFAC-PapersOnLine 48, no. 28 (2015): 1190–95. http://dx.doi.org/10.1016/j.ifacol.2015.12.293.

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Balog, Laszlo, Vasile Berinde, and Mădălina Păcurar. "Approximating Fixed Points of Nonself Contractive Type Mappings in Banach Spaces Endowed with a Graph." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 2 (2016): 27–43. http://dx.doi.org/10.1515/auom-2016-0026.

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Abstract Let K be a non-empty closed subset of a Banach space X endowed with a graph G. We obtain fixed point theorems for nonself G-contractions of Chatterjea type. Our new results complement and extend recent related results [Berinde, V., Păcurar, M., The contraction principle for nonself mappings on Banach spaces endowed with a graph, J. Nonlinear Convex Anal. 16 (2015), no. 9, 1925-1936; Balog, L., Berinde, V., Fixed point theorems for nonself Kannan type contractions in Banach spaces endowed with a graph, Carpathian J. Math. 32 (2016), no. 3 (in press)] and thus provide more general and f

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Thangathamizh R,. "Some Compatible and Weakly-Compatible Four Self-Mapping Results Approach to Nonlinear Integral Equations in Revised Fuzzy Cone Metric Spaces." Advances in Nonlinear Variational Inequalities 28, no. 6s (2025): 207–27. https://doi.org/10.52783/anvi.v28.4146.

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Fixed-point theory plays a vital role in mathematical analysis, particularly in metric and fuzzy metric spaces. In recent years, researchers have explored various extensions of fuzzy metric spaces, including the concept of revised fuzzy cone metric (RFCM) spaces, which combine fuzzy metric structures with cone metric space properties. In this study, we investigate the existence of unique common fixed points for four self-mappings in RFCM spaces under specific contraction conditions. Objective The primary goal of this research is to establish unique common fixed-point theorems for four self-map

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Poochinapan, Kanyuta, Sompop Moonchai, Tanadon Chaobankoh, and Phakdi Charoensawan. "Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction." Mathematics 13, no. 10 (2025): 1569. https://doi.org/10.3390/math13101569.

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A new kind of graph-based contraction in a metric space is introduced in this article. We investigate results concerning the best proximity points and fixed points for these contractions, supported by illustrated examples. The practical applicability of our results is demonstrated through particular instances in the setting of integral equations and differential equations. We also describe how a class of third-order boundary value problems satisfying the present contraction can be solved iteratively. To support our findings, we conduct a series of numerical experiments with various third-order

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Jooste, Charl, and Ruthira Naraidoo. "Nonlinear Tax Elasticities And Their Implications For The Structural Budget Balance." Journal of Applied Business Research (JABR) 27, no. 4 (2011): 113. http://dx.doi.org/10.19030/jabr.v27i4.4661.

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<p>Research on tax elasticities in South Africa mainly employs linear models and shows that taxes evolve symmetrically irrespective of the economic cycle. This study extends this research to show that taxes behave asymmetrically and nonlinearly during expansions and contractions. Estimated linear elasticities imply that a one percent expansion in the cycle increases personal income tax, corporate income tax and value added tax by 1.43, 2.52 and 0.99 percent, respectively. However, estimated nonlinear elasticities are significantly different. During an expansion, the above elasticities in

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Martínez-Moreno, Juan, Wutiphol Sintunavarat, and Poom Kumam. "Banach’s Contraction Principle for Nonlinear Contraction Mappings in Modular Metric Spaces." Bulletin of the Malaysian Mathematical Sciences Society 40, no. 1 (2016): 335–44. http://dx.doi.org/10.1007/s40840-016-0387-2.

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Filali, Doaa, and Faizan Ahmad Khan. "Relation-Theoretic Boyd–Wong Contractions of Pant Type with an Application to Boundary Value Problems." Mathematics 13, no. 14 (2025): 2226. https://doi.org/10.3390/math13142226.

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Non-unique fixed-point theorems play a pivotal role in the mathematical modeling to solve certain typical equations, which admit more than one solution. In such situations, traditional outcomes fail due to uniqueness of fixed points. The primary aim of the present article is to investigate a non-unique fixed-point theorem in the framework of a metric space endowed with a local class of transitive binary relations. To obtain our main objective, we introduce a new nonlinear contraction-inequality that subsumes the ideas involved in four noted contraction conditions, namely: almost contraction, B

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43

Altun, Ishak, Gülhan Mınak, and Murat Olgun. "Fixed points of multivalued nonlinear F-contractions on complete metric spaces." Nonlinear Analysis: Modelling and Control 21, no. 2 (2016): 201–10. http://dx.doi.org/10.15388/na.2016.2.4.

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We introduce a new concept for multivalued maps, also called multivalued nonlinear F-contraction, and give a fixed point result. Our result is a proper generalization of some recent fixed point theorems including the famous theorem of Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334(1):132–139, 2007].

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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

Petruşel, Adrian, Gabriela Petruşel, and Jen-Chih Yao. "Fixed point and coincidence point theorems in b-metric spaces with applications." Applicable Analysis and Discrete Mathematics 11, no. 1 (2017): 199–215. http://dx.doi.org/10.2298/aadm1701199p.

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In this paper, we will consider the coincidence point problem for a pair of single-valued operators satisfying to some contraction and expansion type conditions. Existence, uniqueness and qualitative properties of the solution will be presented. The results are based on some fixed point theorems for nonlinear contractions in complete b-metric spaces. An application illustrates the theoretical results.

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46

Rajagopalan, R., Ekta Tamrakar, Fahad S. Alshammari, H. K. Pathak, and Reny George. "Edge Theoretic Extended Contractions and Their Applications." Journal of Function Spaces 2021 (November 9, 2021): 1–11. http://dx.doi.org/10.1155/2021/5157708.

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Edge theoretic extended contractions are introduced and coincidence point theorems and common fixed-point theorems are proved for such contraction mappings in a metric space endowed with a graph. As further applications, we have proved the existence of a solution of a nonlinear integral equation of Volterra type and given a suitable example in support of our result.

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Akylzhanov, Rauan, and Alexis Arnaudon. "Contractions of group representations via geometric quantization." Letters in Mathematical Physics 110, no. 1 (2019): 43–59. http://dx.doi.org/10.1007/s11005-019-01212-9.

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AbstractWe propose a general framework to contract unitary dual of Lie groups via holomorphic quantization of their coadjoint orbits, using geometric quantization. The sufficient condition for the contractibility of a representation is expressed via cocycles on coadjoint orbits. This condition is verified explicitly for the contraction of SU$$_2$$2 into $$\mathbb {H}$$H. We construct two types of contractions that can be implemented on every matrix Lie group with diagonal contraction matrix.

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48

Ammar, Ammar, Ayman A. Hazaymeh та Anwar Bataihah. "Fixed point results in ωt-distance mappings for Geraghty type contractions". International Journal of Neutrosophic Science 26, № 1 (2025): 01–14. https://doi.org/10.54216/ijns.260101.

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In this study, we establish fixed point theorems for Pωt-contractions within b-metric spaces by utilizing ωtdistance mappings. Subsequently, we demonstrate fixed point results pertaining to nonlinear contraction conditions of the Geraghty type, again employing ωt-distance mappings in the context of a complete b-metric space. Additionally, we bolster our findings with appropriate examples to illustrate the applicability of our results.

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49

Guo, Lifang, Salha Alshaikey, Abeer Alshejari, Muhammad Din, and Umar Ishtiaq. "Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics." Fractal and Fractional 9, no. 1 (2025): 37. https://doi.org/10.3390/fractalfract9010037.

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This paper introduces interpolative enriched cyclic Reich–Rus–Ćirić operators in normed spaces, expanding existing contraction principles by integrating interpolation and cyclic conditions. This class of operators addresses mappings with discontinuities or non-self mappings, enhancing the applicability of fixed-point theory to more complex problems. This class of operators expands on existing cyclic contractions, including interpolative Kannan mappings, interpolative Reich–Rus–Ćirić contractions, and other known contractions in the literature. We demonstrate the existence and uniqueness of fix

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50

Hossain, Asik, Mohammad Arif, Salvatore Sessa, and Qamrul Haque Khan. "Nonlinear Relation-Theoretic Suzuki-Generalized Ćirić-Type Contractions and Application to Fractal Spaces." Fractal and Fractional 6, no. 12 (2022): 711. http://dx.doi.org/10.3390/fractalfract6120711.

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In this article, we introduce the idea of relation-theoretic Suzuki-generalized nonlinear contractions and utilized the same to prove some fixed point results in an ℜ-complete partial metric space. Our newly established results are sharpened versions of earlier existing results in the literature. Indeed, we give an application to construct multivalued fractals using a newly introduced contraction in the iterated function space.

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