International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 693-696
doi:10.1155/S0161171285000771
A variant of a fixed point theorem of Browder-Fan and Reich
Department of Mathematics, University of Wyoming, Laramie 82071, Wyoming, USA
Received 8 January 1985
Copyright © 1985 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.
Abstract
Let S be a convex, weakly compact subset of a locally convex Hausdorff space (E,τ) and f:S→E be a continuous multifunction from its weak topology ω to τ. let ρ be a continuous seminorm on (E,τ) and for subsets A, B of E let p(A,B)=inf{p(x−y):x ϵ A, y ϵ B}. In this paper, sufficient conditions are developed for the existence of an x ϵ S satisfying p(x,fx)=p(fx,S). The result is then used to prove several fixed point theorems.