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

Muhammad Tariq; Eskandar Ameer; Amjad Ali; Hasanen A. Hammad; Fahd Jarad; Muhammad Tariq; Eskandar Ameer; Amjad Ali; Hasanen A. Hammad; Fahd Jarad

doi:10.3934/math.2023191

AIMS Mathematics

2023, Volume 8, Issue 2: 3842-3859. doi: 10.3934/math.2023191

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Research article Special Issues

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

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

Received: 09 September 2022 Revised: 19 November 2022 Accepted: 23 November 2022 Published: 29 November 2022
MSC : 46S40, 47H10, 54H25

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.
- fixed point technique,
- multivalued $ F- $contraction,
- $ m- $metric space,
- multivalued mapping,
- nonlinear matrix equations
Citation: Muhammad Tariq, Eskandar Ameer, Amjad Ali, Hasanen A. Hammad, Fahd Jarad. Applying fixed point techniques for obtaining a positive definite solution to nonlinear matrix equations[J]. AIMS Mathematics, 2023, 8(2): 3842-3859. doi: 10.3934/math.2023191

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Abstract

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.

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