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

V. M. Sehgal

International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-4

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 , f x ) = p ( f x , S ) . The result is then used to prove several fixed point theorems.

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:861748

DOI: 10.1155/S0161171285000771

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