Fixed point theorems on perturbed metric space with an application

TL;DR

This paper introduces fixed point theorems in perturbed metric spaces, providing theoretical results and an application to boundary value problems, supported by counterexamples.

Contribution

It establishes new fixed point theorems for perturbed metric spaces and demonstrates their application to differential equations.

Findings

Fixed point theorems are valid in complete perturbed metric spaces.

Counterexamples justify the theorems.

Application to second-order boundary value problems confirms practical relevance.

Abstract

Following the definition of perturbed metric space, in this paper, some fixed point theorems are established for $ F $-perturbed mappings in complete perturbed metric spaces and justify the result by counter example. Finally, an application of this theorem for the existence of a solution for the second-order boundary value problem is given.