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

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  • V. M. Sehgal

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.

Suggested Citation

  • V. M. Sehgal, 1985. "A variant of a fixed point theorem of Browder-Fan and Reich," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 8, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:861748
    DOI: 10.1155/S0161171285000771
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