Some results on generalized mean nonexpansive mapping in complete metric spaces

Abstract

In this paper, we obtain sufficient conditions for the existence of a unique fixed point of $T$- mean nonexpansive mapping and an integral type of $T$- mean nonexpansive mapping. We also obtain sufficient conditions for the existence of coincidence point and common fixed point for a Jungck-type mean nonexpansive mapping in the frame work of a complete metric space. Some examples of $T$-mean nonexpansive and Jungck-type mean nonexpansive mappings which are not mean nonexpansive mapping are given. The result obtained generalizes corresponding results in this direction in the literature.