Fixed point results for generalized almost contractions and application to a nonlinear matrix equation

Abstract

The goal of this paper was to improve some known results of fixed points by using $ w $-distances and properties of locally symmetric $ \mathcal{H} $-transitivity of binary relations. Also, we gave the application of the obtained results for finding the solution of nonlinear matrix equations. Finally, we gave a numerical example to demonstrate the applicability of our results.

Keywords

• generalized almost contraction
• $ w $-distance
• symmetric locally $ \mathcal{h} $-transitive binary relations
• nonlinear matrix equation
• relational metric space