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An Intersection Theorem for Topological Vector Spaces and Applications

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  • Raúl Fierro

    (Pontificia Universidad Católica de Valparaíso)

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.

Suggested Citation

  • Raúl Fierro, 2021. "An Intersection Theorem for Topological Vector Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 118-133, October.
    • Handle: RePEc:spr:joptap:v:191:y:2021:i:1:d:10.1007_s10957-021-01927-7
    DOI: 10.1007/s10957-021-01927-7
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    References listed on IDEAS

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    1. Ravi P. Agarwal & Mircea Balaj & Donal O’Regan, 2018. "Intersection Theorems with Applications in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 761-777, December.
    2. D. T. Luc, 2008. "An Abstract Problem in Variational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 65-76, July.
    3. Ravi P. Agarwal & Mircea Balaj & Donal O’Regan, 2017. "Common Fixed Point Theorems in Topological Vector Spaces via Intersection Theorems," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 443-458, May.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
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