On fixed points of fundamentally nonexpansive mappings in Banach spaces

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and convex, then its the fixed points set is nonempty, closed and convex.