Applying fixed point methodologies to solve a class of matrix difference equations for a new class of operators

Abstract The goal of this paper is to present a new class of operators satisfying the Prešić-type rational η-contraction condition in the setting of usual metric spaces. New fixed point results are also obtained for these operators. Our results generalize, extend, and unify many papers in this direc...
Ausführliche Beschreibung

Abstract The goal of this paper is to present a new class of operators satisfying the Prešić-type rational η-contraction condition in the setting of usual metric spaces. New fixed point results are also obtained for these operators. Our results generalize, extend, and unify many papers in this direction. Moreover, two examples are derived to support and document our theoretical results. Finally, to strengthen our paper and its contribution to applications, some convergence results for a class of matrix difference equations are investigated. Ausführliche Beschreibung