International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 455-460
Some fixed point theorems for set valued directional contraction mappings
Department of Mathematics, University of Wyoming, Laramie 82071, Wyoming, USA
Received 5 July 1979
Copyright © 1980 V. M. Sehgal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a subset of a metric space and let be the class of all nonempty bounded subsets of with the Hausdorff pseudometric . A mapping is a directional contraction iff there exists a real such that for each and , for each , where . In this paper, sufficient conditions are given under which such mappings have a fixed point.