Asymptotic centers and nonexpansive mappings in conjugate Banach spaces

Teck Cheong Lim

Vol. 90 (1980), No. 1, 135–143

DOI: 10.2140/pjm.1980.90.135

Abstract

This paper concerns fixed point theorems for nonexpansive mappings in conjugate Banach spaces. An example shows that there exist fixed-point-free affine isometries on weak^∗ compact convex sets. Asymptotic centers of decreasing net of founded sets in l¹ are shown to be compact and a common fixed point theorem for left reversible topological semigroup of nonexpansive mappings in l¹ is given.

Mathematical Subject Classification 2000

Primary: 47H09

Secondary: 46B99, 47H10

Milestones

Received: 4 October 1979

Revised: 2 November 1979

Published: 1 September 1980