Fixed points and common points for fundamentally nonexpansive mappings on banach spaces

In this paper, we present some fixed point theorems for fundamentally nonexpansive mappings in Banach spaces and give one common fixed point theorem for a commutative family of demiclosed fundamentally nonexpansive mappings on a nonempty weakly compact convex subset of a strictly convex Banach space with the Opial condition and a uniformly convex in every direction Banach space, respectively; moreover, we show that the common fixed points set of such a family of mappings is closed and convex.

Keywords:

Common fixed point , fixed point , Fundamentally nonexpansive mappings , nonexpansive mappings , Opial’s condition , Uniformly convex in every direction Banach spaces