Fixed Point Results on Partial Modular Metric Space

Dipankar Das,Mohammad Saeed Khan,Salvatore Sessa,Santanu Narzary,Yumnam Mahendra Singh

doi:10.3390/axioms11020062

Dipankar Das, Mohammad Saeed Khan + Show 3 more

Open Access

https://doi.org/10.3390/axioms11020062

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Journal: Axioms	Publication Date: Feb 1, 2022
Citations: 3	License type: CC BY 4.0

Affiliation: University of Naples Federico II, Bodoland University

Abstract

In the present paper, we refine the notion of the partial modular metric defined by Hosseinzadeh and Parvaneh to eliminate the occurrence of discrepancies in the non-zero self-distance and triangular inequality. In support of this, we discuss non-trivial examples. Finally, we prove a common fixed-point theorem for four self-mappings in partial modular metric space and an application to our result; the existence of a solution for a system of Volterra integral equations is discussed.

Highlights

In 1992, Matthews [1] initiated the idea of non-zero self-distance by introducing the notion of the partial metric as a part of the study of the denotational semantics of data flow programming languages in a topological model in computer sciences and extended Banach’s contraction principle [2] in such space
In the present paper, we refine the notion of the partial modular metric defined by Hosseinzadeh and Parvaneh to eliminate the occurrence of discrepancies in the non-zero self-distance and triangular inequality
In 2006, Chistyakov [13] introduced the notion of the metric modular on an arbitrary set and the corresponding modular space, which is more general than a metric space, and, based on this, he further studied Lipschitz continuity and a class of superposition operators on modular metric space

Summary

Introduction

In 1992, Matthews [1] initiated the idea of non-zero self-distance by introducing the notion of the partial metric as a part of the study of the denotational semantics of data flow programming languages in a topological model in computer sciences and extended Banach’s contraction principle [2] in such space. Hosseinzadeh and Parvaneh [16] introduced the notion of partial modular metric spaces as a generalization partial metric space and gave some fixed-point results. We refine the concept of the partial modular metric to eliminate the occurrence of discrepancies in the non-zero self-distance and triangular inequality and prove a common fixed-point theorem for four self-mappings with a suitable example. As an application of our result, the existence of a solution for a system of Volterra integral equations is discussed

Preliminaries

Main Results

Conclusions