An Intersection Theorem for Topological Vector Spaces and Applications

Raúl Fierro ()
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Raúl Fierro: Pontificia Universidad Católica de Valparaíso

Journal of Optimization Theory and Applications, 2021, vol. 191, issue 1, No 5, 118-133

Abstract: Abstract We extend, to the framework of topological vector spaces, two results by Horvath and Kuratowski related to conditions for a family of closed sets to have compact and nonempty intersection. This extension enables us to introduce a number of applications such as the existence of maximal elements in preordered spaces, issues related to KKM functions, fixed point theorems, a variant of a matching theorem by Fan, and mainly the improvement of some minimax and variational inequalities.

Keywords: Intersection theorem; KKM map; Matching theorem; Minimax and variational inequalities; 47H08; 47J20; 49J35; 47H10; 47H04 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01927-7

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