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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]

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]

Let $X$ and $Y$ be two normed spaces over fields $\mathbb{F}$ and $\mathbb{K}$, respectively. We prove new generalised hyperstability results for the general linear equation of the form $g(ax+by)=Ag(x)+Bg(y)$, where $g:X\rightarrow Y$ is a mapping and $a,b\in \mathbb{F}$, $A,B\in \mathbb{K}\backslash \{0\}$, using a modification of the method of Brzdęk [‘Stability of additivity and fixed point methods’, Fixed Point Theory Appl.2013 (2013), Art. ID 285, 9 pages]. The hyperstability results of Piszczek [‘Hyperstability of the general linear functional equation’, Bull. Korean Math. Soc.52 (2015), 1827–1838] can be derived from our main result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several types of Ulam-Hyers stability, well-posedness and limit shadowing property of the fixed point problem in M-metric spaces. Also, we give such results for fixed point problems of Banach and Kannan contractive mappings in M-metric spaces and provide two examples to illustrate the results presented herein. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to obtain some new common fixed point theorems for weakly compatible mappings in fuzzy metric spaces (in the sense of Kramosil and Michálek) satisfying new contractive conditions employing the common limit in the range property. Our results generalize and extend some recent results contained in Jain et al. (2012) [12] to generalized contractive conditions under some control functions. In the process, some results about multidimensional common fixed points as coupled/tripled/quadrupled common fixed point results are derived from our main results. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems for weakly compatible mappings in fuzzy metric spaces employing common limit range property with implicit relations. We also furnish some illustrative examples to support our main results. As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Gopal et al. (2011). [ABSTRACT FROM AUTHOR]

Abstract: Recently, Cho et al. [Y.J. Cho, R. Saadati, S.H. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011) 1254–1260] introduced the concept of the -distance in a cone metric space and established some fixed point theorems on -distance. The aim of this paper is to extend and generalize the main results of Cho et al.  and also show some examples to validate our main results. [Copyright &y& Elsevier]

Abstract The main aim of this work is to unify different classes of fuzzy contractive mappings by introducing a new class of fuzzy contractive mappings called fuzzy Z -contractive mappings. For this new class of mappings, suitable conditions are framed to ensure the existence of fixed point in M -complete fuzzy metric spaces (in the sense of George and Veeramani). A comprehensive set of examples are presented to support the claim. [ABSTRACT FROM AUTHOR]