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In this paper, we introduce the notion of orthogonal Z-contraction mappings and prove fixed point theorems for such contraction mappings in orthogonally metric spaces, which are generalizations of fixed point results for Z-contraction mappings in metric spaces. As an application, we apply our main results to show the existence of a unique positive definite solution of a nonlinear matrix equation.

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Abstract: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.

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