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On a conjecture of S. Reich |
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| Authors: | Peter Z Daffer Hideaki Kaneko Wu Li |
| Institution: | Department of Mathematics, Macon College, Macon, Georgia 31297 ; Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia 23529-0077 ; Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia 23529-0077 |
| 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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