Approximating Solutions of Matrix Equations via Fixed Point Techniques

The principal goal of this work is to investigate new sufficient conditions for the existence and convergence of positive definite solutions to certain classes of matrix equations. Under specific assumptions, the basic tool in our study is a monotone mapping, which admits a unique fixed point in the...

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Autores principales:	Rahul Shukla, Rajendra Pant, Hemant Kumar Nashine, Manuel De la Sen
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	nonexpnasive mapping enriched nonexpansive mapping banach space matrix equations Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/1f44f8547dce4553b4e3116a3e0d0044
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spelling	oai:doaj.org-article:1f44f8547dce4553b4e3116a3e0d00442021-11-11T18:15:09ZApproximating Solutions of Matrix Equations via Fixed Point Techniques10.3390/math92126842227-7390https://doaj.org/article/1f44f8547dce4553b4e3116a3e0d00442021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2684https://doaj.org/toc/2227-7390The principal goal of this work is to investigate new sufficient conditions for the existence and convergence of positive definite solutions to certain classes of matrix equations. Under specific assumptions, the basic tool in our study is a monotone mapping, which admits a unique fixed point in the setting of a partially ordered Banach space. To estimate solutions to these matrix equations, we use the Krasnosel’skiĭ iterative technique. We also discuss some useful examples to illustrate our results.Rahul ShuklaRajendra PantHemant Kumar NashineManuel De la SenMDPI AGarticlenonexpnasive mappingenriched nonexpansive mappingbanach spacematrix equationsMathematicsQA1-939ENMathematics, Vol 9, Iss 2684, p 2684 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	nonexpnasive mapping enriched nonexpansive mapping banach space matrix equations Mathematics QA1-939
spellingShingle	nonexpnasive mapping enriched nonexpansive mapping banach space matrix equations Mathematics QA1-939 Rahul Shukla Rajendra Pant Hemant Kumar Nashine Manuel De la Sen Approximating Solutions of Matrix Equations via Fixed Point Techniques
description	The principal goal of this work is to investigate new sufficient conditions for the existence and convergence of positive definite solutions to certain classes of matrix equations. Under specific assumptions, the basic tool in our study is a monotone mapping, which admits a unique fixed point in the setting of a partially ordered Banach space. To estimate solutions to these matrix equations, we use the Krasnosel’skiĭ iterative technique. We also discuss some useful examples to illustrate our results.
format	article
author	Rahul Shukla Rajendra Pant Hemant Kumar Nashine Manuel De la Sen
author_facet	Rahul Shukla Rajendra Pant Hemant Kumar Nashine Manuel De la Sen
author_sort	Rahul Shukla
title	Approximating Solutions of Matrix Equations via Fixed Point Techniques
title_short	Approximating Solutions of Matrix Equations via Fixed Point Techniques
title_full	Approximating Solutions of Matrix Equations via Fixed Point Techniques
title_fullStr	Approximating Solutions of Matrix Equations via Fixed Point Techniques
title_full_unstemmed	Approximating Solutions of Matrix Equations via Fixed Point Techniques
title_sort	approximating solutions of matrix equations via fixed point techniques
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/1f44f8547dce4553b4e3116a3e0d0044
work_keys_str_mv	AT rahulshukla approximatingsolutionsofmatrixequationsviafixedpointtechniques AT rajendrapant approximatingsolutionsofmatrixequationsviafixedpointtechniques AT hemantkumarnashine approximatingsolutionsofmatrixequationsviafixedpointtechniques AT manueldelasen approximatingsolutionsofmatrixequationsviafixedpointtechniques
_version_	1718431869547053056

Approximating Solutions of Matrix Equations via Fixed Point Techniques

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