Some geometric properties related to the fixed point theory for nonexpansive mappings

Jean-Pierre Gossez and Enrique José Lami Dozo

Vol. 40 (1972), No. 3, 565–573

DOI: 10.2140/pjm.1972.40.565

Abstract

The main result of this paper asserts that if a Banach space admits a sequentially weakly continuous duality function, then a condition introduced by Opial to characterize weak limits by means of the norm is satisfied and the space has normal structure in the sense of Brodskii-Milman. This result of geometric nature allows some unification in the fixed point theory for both single-valued and multi-valued non-expansive mappings.

Mathematical Subject Classification 2000

Primary: 47H10

Secondary: 46B05

Milestones

Received: 12 May 1971

Published: 1 March 1972