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Further on Set-Valued Equilibrium Problems and Applications to Browder Variational Inclusions

Author

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  • Boualem Alleche

    (Université de Médéa)

  • Vicenţiu D. Rădulescu

    (King Abdulaziz University
    University of Craiova)

Abstract

In this paper, we introduce some concepts of convexity and semicontinuity for real set-valued mappings similar to those of real single-valued mappings. Then, we obtain different results on the existence of solutions of set-valued equilibrium problems generalizing in a common way several old ones for both single-valued and set-valued equilibrium problems. Applications to Browder variational inclusions, with weakened conditions on the involved set-valued operator, are given.

Suggested Citation

  • Boualem Alleche & Vicenţiu D. Rădulescu, 2017. "Further on Set-Valued Equilibrium Problems and Applications to Browder Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 39-58, October.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:1:d:10.1007_s10957-017-1169-1
    DOI: 10.1007/s10957-017-1169-1
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    References listed on IDEAS

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    1. Boualem Alleche & Vicenţiu D. Rădulescu, 2016. "Solutions and Approximate Solutions of Quasi-Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 629-649, August.
    2. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, July.
    3. Szilárd László & Adrian Viorel, 2015. "Densely Defined Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 52-75, July.
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    Cited by:

    1. Cristina Stamate, 2024. "Vector Equilibrium Problems—A Unified Approach and Applications," Mathematics, MDPI, vol. 12(10), pages 1-21, May.

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