Fixed point theorems for Lipschitzian pseudo-contractive mappings

Abstract

Let X be a Banach space and flcl A mapping U: D^-Xis said to be pseudo-contractive if, for all u,ve D and all r>0, \\u-v 1, and (ii) (I—U)(G) is closed, then U has a fixed point in G. This result yields fixed point theorems for pseudo-contractive mappings in uniformly convex spaces and for strongly pseudo- contractive mappings in reflexive spaces.