Results on contractions of Reich type in graphical b-metric spaces with applications

Abstract

The main purpose of this article is to present some results concerning Reich type contractions in the graph structure in the framework of recently introduced graphical b-metric spaces. Our results are significant extensions and generalizations of some pioneer results in the existing theory. Innovative examples along with directed graphs are propounded to support the newfangled results, making the established theory more comprehensible. Final section is devoted to apply our results to the existence of solutions of some nonlinear problems along with some open problems which may be fruitful for the further scope of the study.