Approximating solutions of matrix equations via fixed point techniques

Rahul Shukla; Rajendra Pant; Hemant Kumar Nashine; Manuel De la Sen

doi:10.3390/math9212684

Approximating solutions of matrix equations via fixed point techniques

Rahul Shukla, Rajendra Pant, Hemant Kumar Nashine, Manuel De la Sen

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Article number	2684
Journal	Mathematics
Volume	9
Issue number	21
DOIs	https://doi.org/10.3390/math9212684
Publication status	Published - 1 Nov 2021
Externally published	Yes

Keywords

Banach space
Enriched nonexpansive mapping
Matrix equations
Nonexpnasive mapping

ASJC Scopus subject areas

Computer Science (miscellaneous)
General Mathematics
Engineering (miscellaneous)

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10.3390/math9212684

Cite this

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AU - De la Sen, Manuel

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AB - 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.

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KW - Enriched nonexpansive mapping

KW - Matrix equations

KW - Nonexpnasive mapping

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Approximating solutions of matrix equations via fixed point techniques

Abstract

Keywords

ASJC Scopus subject areas

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