A relation theoretic <i>m</i>-metric fixed point algorithm and related applications

Muhammad Tariq; Muhammad Arshad; Mujahid Abbas; Eskandar Ameer; Saber Mansour; Hassen Aydi; Muhammad Tariq; Muhammad Arshad; Mujahid Abbas; Eskandar Ameer; Saber Mansour; Hassen Aydi

doi:10.3934/math.2023995

AIMS Mathematics

2023, Volume 8, Issue 8: 19504-19525. doi: 10.3934/math.2023995

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Research article

A relation theoretic m-metric fixed point algorithm and related applications

1.
Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan
2.
Department of Mathematics, GC university lahore, Pakistan
3.
Department of Mathematics, Taiz University, Taiz, Yemen
4.
Department of Mathematics, Umm Al-Qura University, Faculty of Applied sciences, P.O. Box 14035, Holly Makkah 21955, Saudi Arabia; samansour@uqu.edu.sa
5.
Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
6.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
7.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Received: 14 January 2023 Revised: 02 May 2023 Accepted: 08 May 2023 Published: 09 June 2023
MSC : 34A08, 47H10, 54H25

In this article, we introduce the concept of generalized rational type $ F $ -contractions on relation theoretic m-metric spaces (denoted as $ F_{R}^{m} $-contractions, where $ R $ is a binary relation) and some related fixed point theorems are provided. Then, we achieve some fixed point results for cyclic rational type $ F_{R}^{m} $- generalized contraction mappings. Moreover, we state some illustrative numerically examples to show our results are true and meaningful. As an application, we discuss a positive definite solution of a nonlinear matrix equation of the form $ \Lambda = S+\sum\limits_{i = 1}^{\mu }Q_{i}^{\ast }\Xi \left(\Lambda \right) Q_{i} $.
- relation theoretic m-metric,
- generalized rational type $ F_{R}^{m} $-contractions,
- matrix equation
Citation: Muhammad Tariq, Muhammad Arshad, Mujahid Abbas, Eskandar Ameer, Saber Mansour, Hassen Aydi. A relation theoretic m-metric fixed point algorithm and related applications[J]. AIMS Mathematics, 2023, 8(8): 19504-19525. doi: 10.3934/math.2023995

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Abstract

In this article, we introduce the concept of generalized rational type $ F $ -contractions on relation theoretic m-metric spaces (denoted as $ F_{R}^{m} $-contractions, where $ R $ is a binary relation) and some related fixed point theorems are provided. Then, we achieve some fixed point results for cyclic rational type $ F_{R}^{m} $- generalized contraction mappings. Moreover, we state some illustrative numerically examples to show our results are true and meaningful. As an application, we discuss a positive definite solution of a nonlinear matrix equation of the form $ \Lambda = S+\sum\limits_{i = 1}^{\mu }Q_{i}^{\ast }\Xi \left(\Lambda \right) Q_{i} $.

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