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On a conjecture of S. Reich


Authors: Peter Z. Daffer, Hideaki Kaneko and Wu Li
Journal: Proc. Amer. Math. Soc. 124 (1996), 3159-3162
MSC (1991): Primary 47H10
MathSciNet review: 1363454
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Abstract: Simeon Reich (1974) proved that the fixed point theorem for single-valued mappings proved by Boyd and Wong can be generalized to multivalued mappings which map points into compact sets. He then asked (1983) whether his theorem can be extended to multivalued mappings whose range consists of bounded closed sets. In this note, we provide an affirmative answer for a certain subclass of Boyd-Wong contractive mappings.


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Additional Information

Peter Z. Daffer
Affiliation: Department of Mathematics, Macon College, Macon, Georgia 31297
Email: pdaffer@cennet.mc.peachnet.edu

Hideaki Kaneko
Affiliation: Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia 23529-0077
Email: kaneko@math.odu.edu

Wu Li
Affiliation: Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia 23529-0077
Email: wuli@math.odu.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03659-3
Received by editor(s): April 5, 1995
Communicated by: Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society