The Structure of Fixed Points Set of a Type of Generalized Nonexpansive Mappings in Convex Metric Spaces

In this paper, we show that the fixed points set of self-mappings satisfying condition (C) on a nonempty closed convex subset of a convex metric space having property (D) is always closed and convex. Moreover, we prove that the fixed points set of such mappings on a nonempty bounded closed convex subset of a uniformly convex complete metric space is always nonempty, closed and convex. Our results improve and extend some results in the literature.