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The aim of this work is to introduce the notion of weak altering distance functions and prove new fixed point theorems in metric spaces endowed with a transitive binary relation by using weak altering distance functions. We give some examples which support our main results where previous results in literature are not applicable. Then the main results of the paper are applied to the multidimensional fixed point results. As an application, we apply our main results to study a nonlinear matrix equation. Finally, as numerical experiments, we approximate the definite solution of a nonlinear matrix equation using MATLAB.

The aim of this paper is to introduce the concept of a new nonlinear multi-valued mapping so called weakly (α, ψ, ξ)-contractive mapping and prove fixed point results for such mappings in metric spaces. Our results unify, generalize and complement various results from the literature. We give some examples which support our main results while previous results in literature are not applicable. Also, we analyze the existence of fixed points for mappings satisfying a general contractive inequality of integral type. Many fixed point results for multi-valued mappings in metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph are given here to illustrate the results in this paper.

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]

In this paper, we introduce the notion of $$\alpha $$ -integral type G-contraction mappings to generalize the notions of Banach G-contraction and integral G-contraction mappings. We also prove some fixed point theorems for $$\alpha $$ -integral type G-contraction mappings. By providing some example, we show that our results are real generalization of several results in literature. [ABSTRACT FROM AUTHOR]

The aim of this work is to establish a new fixed point theorem for generalized contraction mappings with respect to w-distances in complete metric spaces. An illustrative example is provided to advocate the usability of our results. Also, we give a numerical experiment for approximating a fixed point in these examples. As an application, the received results are used to summarize the existence and uniqueness of the solution for nonlinear integral equations and nonlinear fractional differential equations of Caputo type. [ABSTRACT FROM AUTHOR]