More general contractions in perturbed metric spaces

TL;DR

This paper introduces two new classes of contractive mappings in perturbed metric spaces, providing fixed point results that generalize existing theorems and illustrating their properties with examples.

Contribution

The paper defines $ ext{phi}$-perturbed and perturbed Kannan mappings, proving fixed point theorems that extend previous results in the field.

Findings

Fixed point results for new mappings

Examples demonstrating generality of results

Perturbed Kannan mappings may lack continuity

Abstract

In the present paper, we introduce two new types of contractive mappings in perturbed metric spaces, namely $\varphi$-perturbed mappings and perturbed Kannan mappings. We prove a fixed point result for such mappings and show that our results are more general then the existing ones. We give an example to illustrate that our results are more general then the existing results and show that perturbed Kannan mappings are not necessarily continuous.