General contractions in new type perturbed metric spaces

TL;DR

This paper introduces a new class of contraction mappings called new type perturbed Kannan mappings within perturbed metric spaces, establishing a fixed point theorem that does not require the operator to be continuous.

Contribution

It generalizes Banach's fixed point theorem to new type perturbed metric spaces using non-continuous contraction mappings.

Findings

Banach's fixed point theorem holds for new type perturbed Kannan mappings.

The fixed point theorem does not depend on the continuity of the operator.

Introduces a novel contraction mapping in perturbed metric spaces.

Abstract

We focus on the new type perturbed metric spaces and introduce a contraction mapping namely new type perturbed Kannan mappings. For these mappings, we show that Banach's fixed point theorem holds. Moreover, this new generalization of Banach's contraction principle does not depend on the continuity of the operator.