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

Tariq, Muhammad Atiq Ur Rehman; Ameer, Eskandar; Ali, Amjad; Hammad, Hasanen A.; Jarad, Fahd

doi:10.3934/math.2023191

Cited by 3 publications

(2 citation statements)

References 32 publications

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“…In the past few decades, many authors have extended and generalized the Banach contraction mapping principle in several ways (see [2][3][4][5][6][7][8][9][10][11][12]). On the other hand, several authors, such as Boyd and Wong [13], Browder [14], Wardowski [15], Jleli and Samet [16], and many other researchers have extended the Banach contraction principle by employing different types of control functions (see [17][18][19][20][21] and the references therein). Alam et al [22] introduced the concept of the relation-theoretic contraction principle and proved some well known fixed-point results in this area.…”

Section: Introductionmentioning

confidence: 99%

“…One of the latest extensions of metric spaces and partial metric spaces [10] was given in paper [28], which completed the concept of m-metric spaces. Using this concept, several researchers have proven some fixed point results in this area (see [20,[29][30][31][32][33]). Subsequently, since every F-contraction mapping is contractive and also continuous, Secelean et al [34] proved that the continuity of an F-contraction can be obtained from condition F 2 .…”

Section: Introductionmentioning

confidence: 99%

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On Relational Weak Fℜm,η-Contractive Mappings and Their Applications

et al. 2023

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In this article, we introduce the concept of weak Fℜm,η-contractions on relation-theoretic m-metric spaces and establish related fixed point theorems, where η is a control function and ℜ is a relation. Then, we detail some fixed point results for cyclic-type weak Fℜm,η-contraction mappings. Finally, we demonstrate some illustrative examples and discuss upper and lower solutions of Volterra-type integral equations of the form ξα=∫0αAα,σ,ξσmσ+Ψα,α∈0,1.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Relational Weak Fℜm,η-Contractive Mappings and Their Applications

et al. 2023

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Certain new iteration of hybrid operators with contractive $ M $ -dynamic relations

Ali

Arshad

Ameer

et al. 2023

MATH

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<abstract>This article investigates Wardowski's contraction in the setting of extended distance spaces known as $ M $-metric spaces using hybrid operators based an $ M $ -dynamic iterative process. The main purpose is to observe new set-valued Chatterjea type common fixed point theorems for hybrid operators with respect to an $ M $-dynamic iterative process, i.e., $ \check{D}(\Psi _{1}, \Psi _{2}, s_{0}) $. We realize an application: the existence of a solution for a multistage system and integral equation. Also, we give a graphical interpretation of our obtained theorems. The main results are explicated with the help of a relevant example. Some important corollaries are extracted from the main theorems as well.</abstract>

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

Tariq

Arshad

Abbas

et al. 2023

MATH

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<abstract>In this article, we introduce the concept of generalized rational type $ F $ -contractions on relation theoretic <italic>m</italic>-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} $.</abstract>

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

Cited by 3 publications

References 32 publications

On Relational Weak Fℜm,η-Contractive Mappings and Their Applications

On Relational Weak Fℜm,η-Contractive Mappings and Their Applications

Certain new iteration of hybrid operators with contractive $ M $ -dynamic relations

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

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