International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1985 / Article

Open Access

Volume 8 |Article ID 861748 | https://doi.org/10.1155/S0161171285000771

V. M. Sehgal, "A variant of a fixed point theorem of Browder-Fan and Reich", International Journal of Mathematics and Mathematical Sciences, vol. 8, Article ID 861748, 4 pages, 1985. https://doi.org/10.1155/S0161171285000771

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

Received08 Jan 1985

Abstract

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.

Copyright © 1985 Hindawi Publishing Corporation. 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.


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