International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 693-696

A variant of a fixed point theorem of Browder-Fan and Reich

V. M. Sehgal

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.


Let S be a convex, weakly compact subset of a locally convex Hausdorff space (E,τ) and f:SE 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(xy):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.