Multivalued nonexpansive mappings and Opial’s condition

Lami Dozo, E.

doi:10.1090/S0002-9939-1973-0310718-0

Multivalued nonexpansive mappings and Opial’s condition
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Proc. Amer. Math. Soc. 38 (1973), 286-292 Request permission

Abstract:

We give relations between a condition introduced by Z. Opial which characterizes weak limits by means of the norm in some Banach spaces and approximations of the identity, in particular for systems of projections. Finally a fixed point theorem for multivalued nonexpansive mappings in a Banach space satisfying this condition is proved; this result generalizes those of J. Markin and F. Browder.

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