On some fixed points of generalized contractions with rational expressions and applications

Abstract

In this paper, we study some results of existence and uniqueness of fixed points for a class of operators satisfying an inequality of rational expressions. We prove that they are Picard mappings. Under certain conditions imposed on the parameters of the inequality, the F-quasi nonexpansive framework of this class is established. Mann and Ishikawa iterative methods are investigated in the framework of convex metric spaces.