On a conjecture of S. Reich-Reference-Cited by-同舟云学术

On a conjecture of S. Reich

Published:1996 Issue:10 Volume:124 Page:3159-3162
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Daffer Peter,Kaneko Hideaki,Li Wu

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1996-124-10/S0002-9939-96-03659-3/S0002-9939-96-03659-3.pdf

Reference8 articles.

1. On nonlinear contractions;Boyd, D. W.;Proc. Amer. Math. Soc.,1969

2. T. H. Chang, Common Fixed Point Theorems for Multi-Valued Mappings,Math. Japonica 41 (1995), 311–320.

3. P. Z. Daffer and H. Kaneko, Fixed Points of Generalized Contractive Multi-Valued Mappings,J. Math. Anal. Appl. 192 (1995), 655–666.

4. Fixed point theorems for multivalued mappings on complete metric spaces;Mizoguchi, Noriko;J. Math. Anal. Appl.,1989

5. Fixed points of contractive functions;Reich, Simeon;Boll. Un. Mat. Ital. (4),1972

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