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

Abstract

The aim of this work is to introduce the concept of an $$(F,\gamma )_{\mathfrak {R}}$$ -contraction which is a weak idea of an F-contraction in metric spaces endowed with a binary relation. Fixed point results for such new contractions are investigated, and its benefit is showing from an example. As applications, we apply theoretical results together with the Thompson metric for solving nonlinear matrix equations. Finally, we give a numerical example showing the usage of the proposed algorithm to solve nonlinear matrix equations.