New generalization of contraction mapping by new control function

TL;DR

This paper introduces a new generalization of contraction mappings using a novel control function and altering distance, establishing fixed point existence results that unify and extend previous findings.

Contribution

The paper presents a new generalization of contraction mappings with a novel control function, broadening fixed point theory.

Findings

Established existence results for the new class of mappings.

Unified and extended previous fixed point theorems.

Reproduced several known and new results in the literature.

Abstract

In this paper, we introduce the new generalization of contraction mapping by a new control function and an altering distance . We establish some existence results of fixed point for such mappings. Our results reproduce several old and new results in the literature.