Existence of fixed point and best proximity point of p-cyclic orbital phi-contraction map

In this manuscript, p-cyclic orbital ϕ-contraction map over closed, nonempty, convex subsets of a uniformly convex Banach space X possesses a unique best proximity point if the auxiliary function ϕ is strictly increasing. The given result unifies and extend some existing results in the related literature. We provide an illustrative example to indicate the validity of the observed result.

Best proximity point theorems for $ \alpha^{+} F, (\theta-\phi )$-proximal contraction

In this paper, inspired by the idea of Suzuki type $ \alpha^{+} F$-proximal contraction in metric spaces, we prove a new existence of best proximity point for Suzuki type $ \alpha^{+} F$-proximal contraction and $ \alpha^{+} (\theta-\phi )$-proximal contraction defined on a closed subset of a complete metric space. Our theorems extend, generalize, and improve many existing results.

On Some Coincidence Best Proximity Point Results

In this paper, we discuss some (coincidence) best proximity point results for generalized proximal contractions and λ − μ -proximal Geraghty contractions in controlled metric type spaces. To clarify our study, various examples are given and some conclusions are drawn.

Best Proximity Point Theorems for Single and Multivalued Mappings in Fuzzy Multiplicative Metric Space

In this paper, we introduce fuzzy multiplicative metric space and prove some best proximity point theorems for single-valued and multivalued proximal contractions on the newly introduced space. As corollaries of our results, we prove some fixed-point theorems. Also, we present best proximity point theorems for Feng-Liu-type multivalued proximal contraction in fuzzy metric space. Moreover, we illustrate our results with some interesting examples.

Existence of Best Proximity Point with an Application to Nonlinear Integral Equations

Using the idea of modified ϱ -proximal admissible mappings, we derive some new best proximity point results for ϱ − ϑ -contraction mappings in metric spaces. We also provide some illustrations to back up our work. As a result of our findings, several fixed-point results for such mappings are also found. We obtain the existence of a solution for nonlinear integral equations as an application.

Best proximity point results and application to a system of integro-differential equations

In this work, we solve the system of integro-differential equations (in terms of Caputo–Fabrizio calculus) using the concepts of the best proximity pair (point) and measure of noncompactness. We first introduce the concept of cyclic (noncyclic) Θ-condensing operator for a pair of sets using the measure of noncompactness and then establish results on the best proximity pair (point) on Banach spaces and strictly Banach spaces. In addition, we have illustrated the considered system of integro-differential equations by three examples and discussed the stability, efficiency, and accuracy of solutions.

Existence of best proximity points satisfying two constraint inequalities

In this paper, we prove the existence of best proximity point and coupled best proximity point on metric spaces with partial order for weak proximal contraction mappings such that these critical points satisfy some constraint inequalities.

A solution to nonlinear Fredholm integral equations in the context of w-distances

In this paper we propose a solution to the nonlinear Fredholm integral equations in the context of w-distance. For this purpose, we also provide a fixed point result in the same setting. In addition, we provide best proximity point results. We give examples and present numerical results to approximate fixed points.