C*-Algebra Valued Modular G-Metric Spaces with Applications in Fixed Point Theory

Dipankar Das,Francisco Eneldo López Monteagudo,Edgar González Fernández,Hamurabi Gamboa Rosales,Lakshmi Narayan Mishra,Arvind Dhaka,Vishnu Narayan Mishra,Tania A Ramirez-Delreal

doi:10.3390/sym13112003

Abstract

This article introduces a new type of C*-algebra valued modular G-metric spaces that is more general than both C*-algebra valued modular metric spaces and modular G-metric spaces. Some properties are also discussed with examples. A few common fixed point results in C*-algebra valued modular G-metric spaces are discussed using the “C*-class function”, along with some suitable examples to validate the results. Ulam–Hyers stability is used to check the stability of some fixed point results. As applications, the existence and uniqueness of solutions for a particular problem in dynamical programming and a system of nonlinear integral equations are provided.

Highlights

In recent years, C∗-algebra has attracted a lot of interest due to its prospective applications in modern mathematics, entropy analysis, fixed point theory, noncommutative geometry, string theory, quantum mechanics, and other fields
Proceeding as in ([59,60]) one can construct the same result in quasi C∗-avmMS instead of C∗-avmGMS
We introduce C∗-avmGMS with some properties and examples

Summary

Introduction

C∗-algebra has attracted a lot of interest due to its prospective applications in modern mathematics, entropy analysis, fixed point theory, noncommutative geometry, string theory, quantum mechanics, and other fields. Ma et al [3] initiated C∗-avMS by replacing real numbers with positive elements of unital C∗-algebra, which generalizes metric spaces, and studied some fixed point results. The foregoing research leads us to investigate modular G-metric spaces in C∗-algebra in order to generalize the existing spaces. The study of such spaces resulted in the generalization of modular Gmetric spaces as well as C∗-avGMS. We introduce C∗-algebra valued modular G-metric spaces via “C∗-class function” to generalize the fixed point results and to offer possible improvements on the structures of some types of metric spaces in algebraic topology. Applications for existence and uniqueness results for a system of nonlinear integral equations and functional equations in dynamic programming are discussed

Preliminaries

Applications

Conclusions