On solving nonlinear matrix equations in terms of b-simulation functions in b-metric spaces with numerical solutions.

The purpose of this paper is to improve the notion of a Z-contraction mapping with respect to a b-simulation function and also prove fixed point results on b-metric spaces endowed with only a transitive relation. Our results can reduce to several important results in the literature. As applications, we extend and generalize Ran and Reurings's results to prove nonlinear matrix equations by giving new notions concerning b-simulation functions. Finally, we give some numerical examples to support some results of our applications. [ABSTRACT FROM AUTHOR]