Applying fixed point techniques for obtaining a positive definite solution to nonlinear matrix equations-Reference-Cited by-同舟云学术

Applying fixed point techniques for obtaining a positive definite solution to nonlinear matrix equations

Published:2023 Issue:2 Volume:8 Page:3842-3859
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Tariq Muhammad¹,Ameer Eskandar²,Ali Amjad¹,Hammad Hasanen A.³⁴,Jarad Fahd⁵⁶

Affiliation:

1. Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan

2. Department of Mathematics, Taiz University, Taiz 6803, Yemen

3. Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia

4. Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt

5. Department of Mathematics, Çankaya University, Etimesgut 06790, Ankara, Turkey

6. Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Abstract

<abstract><p>In this manuscript, the concept of rational-type multivalued $ F- $contraction mappings is investigated. In addition, some nice fixed point results are obtained using this concept in the setting of $ MM- $spaces and ordered $ MM- $spaces. Our findings extend, unify, and generalize a large body of work along the same lines. Moreover, to support and strengthen our results, non-trivial and extensive examples are presented. Ultimately, the theoretical results are involved in obtaining a positive, definite solution to nonlinear matrix equations as an application.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference35 articles.

1. A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435–1443. https://doi.org/10.1090/S0002-9939-03-07220-4

2. S. B. Nadler, Multivalued contraction mappings, Pac. J. Math., 30 (1969), 475–488.

3. S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales, Fund. Math., 3 (1922), 133–181. https://doi.org/10.4064/fm-3-1-133-181

4. E. Ameer, H. Aydi, M. Arshad, H. Alsamir, M. S. Noorani, Hybrid multivalued type contraction mappings in $\alpha_K$-complete partial $b-$metric Spaces and applications, Symmetry, 11 (2019), 86. https://doi.org/10.3390/sym11010086

5. H. Aydi, M. Abbas, C. Vetro, Partial hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topol. Appl., 159 (2012), 3234–3242. https://doi.org/10.1016/j.topol.2012.06.012

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On Relational Weak Fℜm,η-Contractive Mappings and Their Applications;Symmetry;2023-04-15

2. Certain new iteration of hybrid operators with contractive $ M $ -dynamic relations;AIMS Mathematics;2023

3. A relation theoretic <i>m</i>-metric fixed point algorithm and related applications;AIMS Mathematics;2023