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The purpose of this paper is to introduce the numerical algorithm for approximation the solutions of nonlinear matrix equations with the relation-theoretic contractions. First, we introduce the new contraction namely (ψ, φ, R)-contraction and prove the fixed point theorem for relationtheoretic (ψ, φ, R)-contractions in a metric space endowed with a T-orbital transitivity. We also give an example to show the benefit of our theorems. As applications, we apply our main results together with the Thompson metric to solve the nonlinear matrix equations Xr = Q+∑i=1m Ai* Gi(X)Ai, Where r ≥1, Q is an n x n positive definite matrix, Ai is an nx, non-singular matrix with its conjugate transpose Ai* and Gi is a continuous order preserving mapping from a set of all n x n positive definite matrices into itself for all i=1,2,3....,m. Finally, we furnish a numerical example to support results of our applications. [ABSTRACT FROM AUTHOR]

In this paper, the new modified Picard-FB iterative algorithm based on the idea of the iterative algorithm of Fukhar-ud-din and Berinde in [H. Fukhar-ud-dina, V. Berinde, Iterative methods for the class of quasicontractive type operators and comparsion of their rate of convergence in convex metric spaces, Filomat 30 (2016), 223-230.] is defined. We also introduce the class of conditional quasi-contractive mappings in convex metric spaces and prove the convergence result of the purposed iterative algorithm for approximating the fixed points for conditional quasi-contractive mappings in convex metric spaces. Furthermore, a comparison result of the rate of convergence of the new purposed iterative algorithm, the iterative algorithm of Fukhar-ud-din and Berinde and many iterative algorithms in convex metric spaces is investigated. [ABSTRACT FROM AUTHOR]

In 2014, Asadi et al. introduced the concept of an M -metric space which is a generalization of a partial metric space and established Banach and Kannan fixed point theorems on M -metric spaces. In this work, we prove two fixed point theorems for Chatterjea contraction mappings in the framework of M -metric spaces. These provide partial answers to a question posed by Asadi et al. concerning a fixed point for Chatterjea contraction mappings. We also give some examples and numerical results which can be obtained from our results. [ABSTRACT FROM AUTHOR]

Recently, Asadi et al. [M. Asadi, E. Karapinar, P. Salimi, New extension of p-metric spaces with some fixed-point results on M-metric spaces, Journal of Inequalities and Applications, 18 (2014)] introduced and studied the concept of an M-metric space and proved Banach and Kannan fixed point results in complete M-metric spaces. In this work, we establish some fixed point results for nonlinear contractive mappings by utilizing the control functions which were initiated by Sintunavarat et al. [W. Sintunavarat, Y. J. Cho, P. Kumam, Common fixed point theorems for c-distance in ordered cone metric spaces, Computers and Mathematics with Applications, 62 (2011) 1969-1978]. Presented theorems extend and generalize many existing results in the literature. We also give some illustrative examples. [ABSTRACT FROM AUTHOR]

The aim of this work is to introduce notions of a modification of the common limit in the range property and two generalized multi-valued F-contraction mappings in metric spaces. Fixed point results with two concepts mentioned above are established. Also, we give an example to illustrate our main results. As applications, we prove the existence of a common solution for the system of functional equations in dynamic programming. [ABSTRACT FROM AUTHOR]

In this work, we introduce the concept of an s-simulation function, where s is a given real number with $$s \ge 1$$ , and use this concept for proving many results in b-metric spaces. One of these results is the existence and uniqueness of a fixed point for nonlinear mappings involving s-simulation functions. Also, we give some examples to illustrate the main results with some numerical results. Our results generalize and improve many results in b-metric spaces and also in metric spaces. [ABSTRACT FROM AUTHOR]

The purpose of this work is to introduce the new contractive condition which involves mw-distances in metric spaces. The fixed point theorems for mappings satisfying such contractive condition are established via the idea of an adapting-ceiling distance. Two illustrative examples are also given to confirm that our results rightly generalize many results in the literatures. As an application, the existence and uniqueness of the solution for nonlinear Fredholm integral equations and nonlinear Volterra integral equations are investigated via our main result. [ABSTRACT FROM AUTHOR]

In (Fixed Point Theory Appl 94:6, 2012), the author introduced a new kind of contractions, called F- contractions, that extended the Banach contractions in a newfangled way. In this work, we introduce the notion of $$F_\mathfrak {R}$$ - contraction where $$\mathfrak {R}$$ is a binary relation on its domain that has not to be neither transitive nor a partial order. Consequently, we establish some fixed point results for such contractions in complete metric spaces that improve the Wardowski's original idea and we also give illustrative examples. Furthermore, we show some results to guarantee existence and uniqueness of fixed point of N-order. As an application, we apply our main result to study a class of nonlinear matrix equation. [ABSTRACT FROM AUTHOR]