Solving a class of nonlinear matrix equations via the coupled fixed point theorem

Asgari, Mohammad Sadegh; Mousavi, Baharak

doi:10.1016/j.amc.2015.02.049

Cited by 5 publications

(4 citation statements)

References 19 publications

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“…Therefore, t = 1. Hence, ϕ(1) ≥ η (1). Consequently, the conclusion of Corollary 2 in [14] can also be obtained from Theorem 3.…”

Section: Fixed-point Theory In the Setting Of Non-archimedean Fuzzy Metric Spacessupporting

confidence: 52%

“…Fixed-point theory has become one of the most attractive fields in nonlinear analysis and even mathematics in general, due to its ability to find solutions of nonlinear equations, such as functional equations, matrix equations [1][2][3][4], integral equations [5][6][7], etc. Therefore, it is an essential and powerful tool for solving some existence problems because of its wide applications in areas such as computer science, engineering, economics, physics, game theory and many other fields.…”

Section: Introductionmentioning

confidence: 99%

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A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

et al. 2021

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Very recently, by considering a self-mapping T on a complete metric space satisfying a general contractivity condition of the form ψ(d(Tx,Ty))≤φ(d(x,y)), Proinov proved some fixed-point theorems, which extended and unified many existing results in the literature. Accordingly, inspired by Proinov-type contraction conditions, Roldán López de Hierro et al. introduced a novel family of contractions in fuzzy metric spaces (in the sense of George and Veeramani), whose main advantage is the very weak constraints imposed on the auxiliary functions that appear in the contractivity condition. They also proved the existence and uniqueness of fixed points for the discussed family of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces. In this paper, we introduce a new family of fuzzy contractions based on Proinov-type contractions for which the involved auxiliary functions are not supposed to satisfy any monotonicity assumptions; further, we establish some new results about the existence and uniqueness of fixed points. Furthermore, we show how the main results in the above-mentioned paper can be deduced from our main statements. In this way, our conclusions provide a positive partial solution to one of the open problems posed by such authors for deleting or weakening the hypothesis of the nondecreasingness character of the auxiliary functions.

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“…Therefore, t = 1. Hence, ϕ(1) ≥ η (1). Consequently, the conclusion of Corollary 2 in [14] can also be obtained from Theorem 3.…”

Section: Fixed-point Theory In the Setting Of Non-archimedean Fuzzy Metric Spacessupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

et al. 2021

View full text Add to dashboard Cite

show abstract

“…In recent years, fixed-point theory has become a tantalizing field of research in nonlinear analysis due to its wide range of applications in computer sciences, game theory, physics, economics, and various other fields. It has become a tool to find solutions for nonlinear equations such as differential equations, integrodifferential equations, and matrix equations [1,2]. After the fundamental Banach's theorem [3] in 1922, a huge amount of literature appeared for the investigation of fixed points of self-operators.…”

Section: Introductionmentioning

confidence: 99%

κ_G‐Contractive Mappings in Fuzzy Metric Spaces

Samreen

Hussain

Aydi

et al. 2022

Journal of Mathematics

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“…Coupled fixed point theorem is one of the most heavily used tools to solve nonlinear matrix equations. In this setting Liu and Chen [18], Berzig et al [3], Hasanov [14], Asgari and Mousavi [2] and many more used this tool to compute the solutions of different groups of nonlinear matrix equations.…”

Section: Introductionmentioning

confidence: 99%

Solutions of a class of nonlinear matrix equations

Pakhira,

Bose,

Hossein

2019

Preprint

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In this article we present several necessary and sufficient conditions for the existence of Hermitian positive definite solutions of nonlinear matrix equations of the form X s + A * X −t A + B * X −p B = Q, where s, t, p ≥ 1, A, B are nonsingular matrices and Q is a Hermitian positive definite matrix. We derive some iterations to compute the solutions followed by some examples. In this context we also discuss about the maximal and the minimal Hermitian positive definite solution of this particular nonlinear matrix equation.

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Solving a class of nonlinear matrix equations via the coupled fixed point theorem

Cited by 5 publications

References 19 publications

A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

κ_G‐Contractive Mappings in Fuzzy Metric Spaces

Solutions of a class of nonlinear matrix equations

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Solving a class of nonlinear matrix equations via the coupled fixed point theorem

Cited by 5 publications

References 19 publications

A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

κG‐Contractive Mappings in Fuzzy Metric Spaces

Solutions of a class of nonlinear matrix equations

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Product

Resources

About

κ_G‐Contractive Mappings in Fuzzy Metric Spaces