Proximity Point Theorems Research Articles

Approximate best proximity point sequences for C*λ mappings in strictly convex Banach spaces

Let A and B be nonempty subsets of a Banach space X and T : A → B be a non-self mapping. An approximate sequence of best proximity points for the mapping T is a sequence {xn } in A such that lim n →∞ || xn − T xn || → dist(A, B). In the current paper, we survey the existence of approximate best proximity point sequences for single and multivalued non-self mappings in strictly convex Banach spaces. We also introduce a geometric notion on a nonempty and convex pair of subsets of a Banach space, called semi-Opial condition, and establish some new best proximity point theorems.

Best Proximity Results with Applications to Nonlinear Dynamical Systems

Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution ω that is optimal in the sense that the error σ ( ω , J ω ) assumes the global minimum value σ ( θ , ϑ ) . The aim of this paper is to define the notion of Suzuki α - Θ -proximal multivalued contraction and prove the existence of best proximity points ω satisfying σ ( ω , J ω ) = σ ( θ , ϑ ) , where J is assumed to be continuous or the space M is regular. We derive some best proximity results on a metric space with graphs and ordered metric spaces as consequences. We also provide a non trivial example to support our main results. As applications of our main results, we discuss some variational inequality problems and dynamical programming problems.

Proximity Point Properties for Admitting Center Maps

In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:Crightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we show that in some conditions, the set of all best proximity points is nonempty and compact.

Best Proximity Point Results for Quasi Contractions of Perov Type in Non-Normal Cone Metric Space

In this paper, we study the notion of Ciric-Perov quasi contraction and Fisher-Perov quasi contraction and prove some best proximity point theorems for such contractions in the frame work of non-normal regular cone metric spaces. We give an example to support our result. Our results extend and generalized many existing results in literature.

A best proximity point theorem for \u03b1-proximal Geraghty non-self mappings

In this paper, we search some best proximity point results for a new class of non-self mappings T:A longrightarrow B called α-proximal Geraghty mappings. Our results extend many recent results appearing in the literature. We suggest an example to support our result. Several consequences are derived. As applications, we investigate the existence of best proximity points for a metric space endowed with symmetric binary relation.

Best Proximity Point Theorems of C-class Functions in Regular Cone Metric Spaces

Best Proximity Point Theorems of C-class Functions in Regular Cone Metric Spaces

Best Proximity Point Theorems for Two Weak Cyclic Contractions on Metric-Like Spaces

In this paper, we establish two best proximity point theorems in the setting of metric-like spaces that are based on cyclic contraction: Meir–Keeler–Kannan type cyclic contractions and a generalized Ćirić type cyclic φ -contraction via the MT -function. We express some examples to indicate the validity of the presented results. Our results unify and generalize a number of best proximity point results on the topic in the corresponding recent literature.

Best Proximity Point Theorems for Some Special Proximal Contractions

This article explores some new best proximity point theorems for absolute proximal cyclic contractions and dual supreme proximal contractions which are not necessarily continuous. As a consequence of such best proximity point theorems, the famous contraction principle is elicited.

The Convex (\delta,L) Weak Contraction Mapping Theorem and its Non-Self Counterpart in Graphic Language

Let $(X,d)$ be a metric space. A map $T:X \mapsto X$ is said to be a $(\delta,L)$ weak contraction [1] if there exists $\delta \in (0,1)$ and $L\geq 0$ such that the following inequality holds for all $x,y \in X$: $d(Tx,Ty)\leq \delta d (x,y)+Ld(y,Tx)$ On the other hand, the idea of convex contractions appeared in [2] and [3]. In the first part of this paper, motivated by [1]-[3], we introduce a concept of convex $(\delta,L)$ weak contraction, and obtain a fixed point theorem associated with this mapping. In the second part of this paper, we consider the map is a non-self map, and obtain a best proximity point theorem. Finally, we leave the reader with some open problems.

Best Proximity Point Theorems on Rectangular Metric Spaces Endowed with a Graph

In this paper, we ensure the existence and uniqueness of a best proximity point in rectangular metric spaces endowed with a graph structure.

Best Proximity Point Theorems in Metric Spaces

Best Proximity Point Theorems in Metric Spaces

Quadrupled best proximity point theorems in partially ordered metric spaces

In this paper, we prove some quadrupled best proximity point theorems in partially ordered metric space by using (𝜓,𝜙) contraction. Our results generalise the results of Kumam et.al. (Coupled best proximity points in ordered metric spaces, Fixed point Theory and Application 2014, 2014:107). An example is also given to verify the results obtained.

A Best Proximity Point Theorem for G-Proximal (delta, 1-delta) Weak Contraction in Complete Metric Space Endowed with a Graph

The notion of (delta, 1-delta) weak contraction appeared in [1]. In this paper, we consider that the map satisfying the (delta, 1-delta) weak contraction is a non-self map, and obtain a best proximity point theorem in complete metric space endowed with a graph.

Best proximity point theorems in $b$-metric space satisfying rational contractions

Best proximity point theorems in $b$-metric space satisfying rational contractions

Best proximity point theorems for Fρ-proximal contraction in modular function spaces

In this paper, we introduce Wardowski’s F-contractions in the context of modular function spaces. We also introduce the concept of Fρ-proximal contraction and prove some best proximity point theorems by unifying and generalizing some recent results in modular function spaces. Moreover, we discuss some illustrative examples to highlight the realized improvements.

Best proximity point results for Suzuki-Edelstein proximal contractions via auxiliary functions

In this paper we study the notion of modified Suzuki-Edelstein proximal contraction under some auxiliary functions for non-self mappings and obtain best proximity point theorems in the setting of complete metric spaces. As applications, we derive best proximity point and fixed point results for such contraction mappings in partially ordered metric spaces. Some examples are given to show the validity of our results. Our results extend and unify many existing results in the literature.

Best proximity point theorems in b-metric spaces

In this paper, we prove best proximity point theorems for types of cyclic b-contraction mappings in the setting of complete b-metric spaces which generalize some results in the current literature.

Random Best Proximity Points for α-Admissible Mappings via Simulation Functions

In this paper, we introduce a new concept of random α -proximal admissible and random α - Z -contraction. Then we establish random best proximity point theorems for such mapping in complete separable metric spaces.

Best Proximity Point Theorems for a Berinde MT-Cyclic Contraction on a Semisharp Proximal Pair

In this paper, a new type of non-self-mapping, called Berinde MT-cyclic contractions, is introduced and studied. Best proximity point theorems for this type of mappings in a metric space are presented. Some examples illustrating our main results are also given. Our results generalize and improve some known results in the literature.

Best proximity point theorems for some classes of contractions

This article elicits some best proximity point theorems, dealing with a special genre of global minimization problem to produce optimal approximate solutions for nonlinear equations of the form Tx = x, which models many nonlinear phenomena, where T is a C-cyclic contraction, a C-proximal contraction, a K-cyclic contraction or a K-proximal contraction in the frameworks of fairly complete spaces and proximally complete spaces.