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Zbl 0835.54028
Daffer, Peter Z.; Kaneko, Hideaki
Fixed points of generalized contractive multi-valued mappings. (English)
[J] J. Math. Anal. Appl. 192, No.2, 655-666 (1995). ISSN 0022-247X

Summary: In a recent paper {\it N. Mizoguchi} and {\it W. Takahashi} [ibid. 141, No. 1, 177-188 (1989; Zbl 0688.54028)] gave a positive answer to the conjecture of S. Reich concerning the existence of fixed points of multi- valued mappings that satisfy a certain contractive condition. In this paper, we provide an alternative and somewhat more straightforward proof for the theorem of Mizoguchi and Takahashi. Also the problems associated with fixed points of weakly contractive multi-valued mappings are studied. Finally, we make a few comments that improve other results from the paper cited above.

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
54C60 Set-valued maps

Citations: Zbl 0688.54028

Cited in: Zbl 1180.54053 Zbl 1081.47069

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