An application of KKM-map principle

A. Carbone

International Journal of Mathematics and Mathematical Sciences, 1992, vol. 15, 1-3

Abstract:

The following theorem is proved and several fixed point theorems and coincidence theorems are derived as corollaries. Let C be a nonempty convex subset of a normed linear space X , f : C → X a continuous function, g : C → C continuous, onto and almost quasi-convex. Assume that C has a nonempty compact convex subset D such that the set A = { y ∈ C : ‖ g ( x ) − f ( y ) ‖ ≥ ‖ g ( y ) − f ( y ) ‖ for all x ∈ D } is compact.

Then there is a point y 0 ∈ C such that ‖ g ( y 0 ) − f ( y 0 ) ‖ = d ( f ( y 0 ) , C ) .

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:571891

DOI: 10.1155/S0161171292000875

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