| TITLE: |
Fixed Points of Generalized Contractive Multi-valued Mappings |
Author(s): | Peter Z. Daffer and Hideaki Kaneko | Source (status): | Journal of Mathematical Analysis and Applications, Vol. 192, 655-666 (1995). |
Abstract:
In a recent paper, Mizoguchi and Takahashi \cite{MT} 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 of the theorem of Mizoguchi and Takahashi. Also the problems associated with the fixed points of weakly contractive multi-valued mappings are studied. Finally, we make a few comments that improve additional results of Mizoguchi and Takahashi.
{MT} Jl. Math. Anal. Appl. Vol. 141, 177-188 (1989).