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An application of KKM-map principle

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  • A. Carbone

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 ) .

Suggested Citation

  • A. Carbone, 1992. "An application of KKM-map principle," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 15, pages 1-3, January.
    • Handle: RePEc:hin:jijmms:571891
    DOI: 10.1155/S0161171292000875
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    Cited by:

    1. Zoran D. Mitrović & Azhar Hussain & Manuel de la Sen & Stojan Radenović, 2020. "On Best Approximations for Set-Valued Mappings in G -convex Spaces," Mathematics, MDPI, vol. 8(3), pages 1-7, March.

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