ULTRANETS AND FIXED POINT THEOREMS FOR MULTIVALUED NONEXPANSIVE MAPPINGS

A. Kaewcharoen (Thailand)

Received March 7, 2007

Abstract

Let E be a nonempty weakly compact convex subset of a Banach space which satisfies property  i.e., an inequality concerning the asymptotic radii of two ultranets. We prove that a multivalued nonexpansive and -contractive mapping  has a fixed point.

Keywords and phrases: multivalued nonexpansive mapping, inwardness condition, ultranet.