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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Multivalued nonexpansive mappings and Opial's condition


Author: E. Lami Dozo
Journal: Proc. Amer. Math. Soc. 38 (1973), 286-292
MSC: Primary 47H10; Secondary 46B05
DOI: https://doi.org/10.1090/S0002-9939-1973-0310718-0
MathSciNet review: 0310718
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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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DOI: https://doi.org/10.1090/S0002-9939-1973-0310718-0
Keywords: Fixed point theorem, systems of projections, geometric properties of Banach spaces
Article copyright: © Copyright 1973 American Mathematical Society