Daffer, Peter Z.; Kaneko, Hideaki Fixed points of generalized contractive multi-valued mappings. (English) Zbl 0835.54028 J. Math. Anal. Appl. 192, No. 2, 655-666 (1995). Summary: In a recent paper N. Mizoguchi and 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. Cited in 6 ReviewsCited in 99 Documents MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 54C60 Set-valued maps in general topology Citations:Zbl 0688.54028 PDFBibTeX XMLCite \textit{P. Z. Daffer} and \textit{H. Kaneko}, J. Math. Anal. Appl. 192, No. 2, 655--666 (1995; Zbl 0835.54028) Full Text: DOI Link