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

<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...

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Autores principales: Dipankar Das, Lakshmi Narayan Mishra, Vishnu Narayan Mishra, Hamurabi Gamboa Rosales, Arvind Dhaka, Francisco Eneldo López Monteagudo, Edgar González Fernández, Tania A. Ramirez-delReal
Formato: article
Lenguaje:EN
Publicado: MDPI AG 2021
Materias:
<i>C</i>*-class function
<i>mGMS</i>
<i>C</i>*-<i>avMS</i>
<i>C</i>*-<i>avb-MS</i>
<i>C</i>*-<i>avGMS</i>
Ulam–Hyers stability
Mathematics
QA1-939
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spelling oai:doaj.org-article:8ceedba3298f42b2b784d74c98c0eceb2021-11-25T19:05:57Z<i>C</i>*-Algebra Valued Modular <i>G</i>-Metric Spaces with Applications in Fixed Point Theory10.3390/sym131120032073-8994https://doaj.org/article/8ceedba3298f42b2b784d74c98c0eceb2021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2003https://doaj.org/toc/2073-8994This 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.Dipankar DasLakshmi Narayan MishraVishnu Narayan MishraHamurabi Gamboa RosalesArvind DhakaFrancisco Eneldo López MonteagudoEdgar González FernándezTania A. Ramirez-delRealMDPI AGarticle<i>C</i>*-class function<i>mGMS</i><i>C</i>*-<i>avMS</i><i>C</i>*-<i>avb-MS</i><i>C</i>*-<i>avGMS</i>Ulam–Hyers stabilityMathematicsQA1-939ENSymmetry, Vol 13, Iss 2003, p 2003 (2021)
institution DOAJ
collection DOAJ
language EN
topic <i>C</i>*-class function
<i>mGMS</i>
<i>C</i>*-<i>avMS</i>
<i>C</i>*-<i>avb-MS</i>
<i>C</i>*-<i>avGMS</i>
Ulam–Hyers stability
Mathematics
QA1-939
spellingShingle <i>C</i>*-class function
<i>mGMS</i>
<i>C</i>*-<i>avMS</i>
<i>C</i>*-<i>avb-MS</i>
<i>C</i>*-<i>avGMS</i>
Ulam–Hyers stability
Mathematics
QA1-939
Dipankar Das
Lakshmi Narayan Mishra
Vishnu Narayan Mishra
Hamurabi Gamboa Rosales
Arvind Dhaka
Francisco Eneldo López Monteagudo
Edgar González Fernández
Tania A. Ramirez-delReal
<i>C</i>*-Algebra Valued Modular <i>G</i>-Metric Spaces with Applications in Fixed Point Theory
description 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.
format article
author Dipankar Das
Lakshmi Narayan Mishra
Vishnu Narayan Mishra
Hamurabi Gamboa Rosales
Arvind Dhaka
Francisco Eneldo López Monteagudo
Edgar González Fernández
Tania A. Ramirez-delReal
author_facet Dipankar Das
Lakshmi Narayan Mishra
Vishnu Narayan Mishra
Hamurabi Gamboa Rosales
Arvind Dhaka
Francisco Eneldo López Monteagudo
Edgar González Fernández
Tania A. Ramirez-delReal
author_sort Dipankar Das
title <i>C</i>*-Algebra Valued Modular <i>G</i>-Metric Spaces with Applications in Fixed Point Theory
title_short <i>C</i>*-Algebra Valued Modular <i>G</i>-Metric Spaces with Applications in Fixed Point Theory
title_full <i>C</i>*-Algebra Valued Modular <i>G</i>-Metric Spaces with Applications in Fixed Point Theory
title_fullStr <i>C</i>*-Algebra Valued Modular <i>G</i>-Metric Spaces with Applications in Fixed Point Theory
title_full_unstemmed <i>C</i>*-Algebra Valued Modular <i>G</i>-Metric Spaces with Applications in Fixed Point Theory
title_sort <i>c</i>*-algebra valued modular <i>g</i>-metric spaces with applications in fixed point theory
publisher MDPI AG
publishDate 2021
url https://doaj.org/article/8ceedba3298f42b2b784d74c98c0eceb
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