Vol. 40, No. 3, 1972

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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

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
Received: 12 May 1971
Published: 1 March 1972
Jean-Pierre Gossez
Enrique José Lami Dozo