New algorithm for finding the solution of nonlinear matrix equations based on the weak condition with relation-theoretic F-contractions

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Kanokwan Sawangsup ◽  
Wutiphol Sintunavarat
Keyword(s):  
Weak Condition ◽  
Matrix Equations ◽  
Nonlinear Matrix

scholarly journals Positive coincidence points for a class of nonlinear operators and their applications to matrix equations

2020 ◽  
Vol 18 (1) ◽  
pp. 858-872
Author(s):  
Imed Kedim ◽  
Maher Berzig ◽  
Ahdi Noomen Ajmi
Keyword(s):  
Banach Space ◽  
Positive Solution ◽  
Positive Definite ◽  
Positive Cone ◽  
Matrix Equations ◽  
Ordered Banach Space ◽  
Coincidence Points ◽  
Nonlinear Operators ◽  
Nonlinear Matrix

Abstract Consider an ordered Banach space and f,g two self-operators defined on the interior of its positive cone. In this article, we prove that the equation f(X)=g(X) has a positive solution, whenever f is strictly \alpha -concave g-monotone or strictly (-\alpha ) -convex g-antitone with g super-homogeneous and surjective. As applications, we show the existence of positive definite solutions to new classes of nonlinear matrix equations.

scholarly journals Common Fixed-Point Results in Ordered Left (Right) Quasi- b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Hemant Kumar Nashine ◽  
Sourav Shil ◽  
Hiranmoy Garai ◽  
Lakshmi Kanta Dey ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Matrix Equations ◽  
Ordered Sets ◽  
Nonlinear Matrix ◽  
Fractional Differential ◽  
Left And Right

We use the notions of left- and right-complete quasi- b -metric spaces and partial ordered sets to obtain a couple of common fixed-point results for strictly weakly isotone increasing mappings and relatively weakly increasing mappings, which satisfy a pair of almost generalized contractive conditions. To illustrate our results, throughout the paper, we give several relevant examples. Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.

scholarly journals Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 93
Author(s):  
Zhenhua Ma ◽  
Azhar Hussain ◽  
Muhammad Adeel ◽  
Nawab Hussain ◽  
Ekrem Savas
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Positive Definite ◽  
Matrix Equations ◽  
Nonlinear Matrix Equation ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Positive Definite Solution ◽  
Nonlinear Matrix ◽  
Definite Solution

In this paper, we introduce the notion of C ´ iri c ´ type α - ψ - Θ -contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation X = Q + ∑ i = 1 m A i * γ ( X ) A i and give a numerical example.

scholarly journals Solving large-scale nonlinear matrix equations by doubling

2013 ◽  
Vol 439 (4) ◽  
pp. 914-932 ◽  
Author(s):  
Peter Chang-Yi Weng ◽  
Eric King-Wah Chu ◽  
Yueh-Cheng Kuo ◽  
Wen-Wei Lin
Keyword(s):  
Large Scale ◽  
Matrix Equations ◽  
Nonlinear Matrix

scholarly journals Relation Theoretic (Θ,R) Contraction Results with Applications to Nonlinear Matrix Equations

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 767 ◽  
Author(s):  
Hamed Al-Sulami ◽  
Jamshaid Ahmad ◽  
Nawab Hussain ◽  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Binary Relation ◽  
Metric Spaces ◽  
Matrix Equations ◽  
Existence Of A Solution ◽  
Complete Metric Spaces ◽  
Numerical Example ◽  
Nonlinear Matrix

Using the concept of binary relation R , we initiate a notion of Θ R -contraction and obtain some fixed point results for such mappings in the setting of complete metric spaces. Furthermore, we establish some new results of fixed points of N-order. Consequently, we improve and generalize the corresponding known fixed point results. As an application of our main result, we provide the existence of a solution for a class of nonlinear matrix equations. A numerical example is also presented to illustrate the theoretical findings.

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