Fixed point results via a new class of Ad-contractions

TL;DR

This paper introduces Ad-contractions, a new class of operators, extending A-contractions to dislocated metric spaces, and establishes fixed point theorems for various types of mappings within this framework.

Contribution

It generalizes fixed point results for A-contractions to the broader setting of dislocated metric spaces using Ad-contractions.

Findings

Fixed point theorems for single mappings and sequences

Extension to integral type contractions

Applicability to sets with two dislocated metrics

Abstract

In this article, a new class of operators, termed Ad-contractions, is introduced to extend the framework of A-contractions to the setting of dislocated metric spaces. Fixed point results are established for single mappings, sequences of mappings, integral type contractions, and for mappings on a set with two dislocated metrics. The demonstrated theorems generalize foundational results on A-contractions and their integral-type variations to the more challenging setting of dislocated metric spaces. The work is supported by illustrative examples.