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

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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.

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Acknowledgements

V.D. Rădulescu acknowledges the support through a grant of the Ministry of Research and Innovation, CNCS–UEFISCDI, project number PN-III-P4-ID-PCE-2016-0130, within PNCDI III.

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Authors and Affiliations

  1. Laboratoire LPTEA, Faculté des Sciences, Université de Médéa, 26000, Medea, Algeria

    Boualem Alleche

  2. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Vicenţiu D. Rădulescu

  3. Department of Mathematics, University of Craiova, Street A.I. Cuza No 13, 200585, Craiova, Romania

    Vicenţiu D. Rădulescu

Authors
  1. Boualem Alleche
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  2. Vicenţiu D. Rădulescu
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Correspondence to Vicenţiu D. Rădulescu.

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Alleche, B., Rădulescu, V.D. Further on Set-Valued Equilibrium Problems and Applications to Browder Variational Inclusions. J Optim Theory Appl 175, 39–58 (2017). https://doi.org/10.1007/s10957-017-1169-1

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  • DOI: https://doi.org/10.1007/s10957-017-1169-1

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