<i>C</i>*-Algebra Valued Modular <i>G</i>-Metric Spaces with Applications in Fixed Point Theory

This article introduces a new type of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-algebra...

Full description

Saved in:
Bibliographic Details
Main Authors: Dipankar Das, Lakshmi Narayan Mishra, Vishnu Narayan Mishra, Hamurabi Gamboa Rosales, Arvind Dhaka, Francisco Eneldo López Monteagudo, Edgar González Fernández, Tania A. Ramirez-delReal
Format: article
Language:EN
Published: MDPI AG 2021
Subjects:
Online Access:https://doaj.org/article/8ceedba3298f42b2b784d74c98c0eceb
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This article introduces a new type of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-algebra valued modular <i>G</i>-metric spaces that is more general than both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-algebra valued modular metric spaces and modular <i>G</i>-metric spaces. Some properties are also discussed with examples. A few common fixed point results in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-algebra valued modular <i>G</i>-metric spaces are discussed using the “<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mo>*</mo></msub></semantics></math></inline-formula>-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.