Common Fixed Point Theorems on LR-$(\delta,\phi)$ Quasi Partial $b$-Metric Spaces

TL;DR

This paper introduces a new class of metric spaces called LR-$( extdelta, extphi)$ quasi partial $b$-metric spaces and proves a common fixed point theorem within this framework, supported by an illustrative example.

Contribution

The paper defines LR-$( extdelta, extphi)$ quasi partial $b$-metric spaces and establishes a fixed point theorem for these spaces, expanding fixed point theory.

Findings

Established the fixed point theorem in complete LR-$( extdelta, extphi)$ quasi partial $b$-metric spaces.

Provided a non-trivial example illustrating the concepts.

Extended the scope of fixed point results to new generalized metric spaces.

Abstract

In this article, we introduce the LR-$(\delta,\phi)$ quasi partial $b$-metric space. Also, the common fixed point theorem on complete LR-$(\delta,\phi)$ quasi partial $b$-metric space has been proved. A non-trivial example is also given.