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Proceedings of the American Mathematical Society

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



An iteration process for nonexpansive mappings with applications to fixed point theory in product spaces

Author: W. A. Kirk
Journal: Proc. Amer. Math. Soc. 107 (1989), 411-415
MSC: Primary 47H10; Secondary 47H09
MathSciNet review: 941325
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Abstract: A uniform transfinite iteration procedure for selecting fixed points of nonexpansive mappings is introduced. This procedure, which applies to arbitrary nonexpansive mappings in Banach spaces having Kadec-Klee norm and to strictly contractive mappings in reflexive Banach spaces, is used to generalize a fixed point theorem of Kirk and Sternfeld for nonexpansive mappings in product spaces.

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Keywords: Nonexpansive mappings, fixed points, product spaces
Article copyright: © Copyright 1989 American Mathematical Society