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Further on set-valued equilibrium problems in the pseudo-monotone case and applications to Browder variational inclusions

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Abstract

This paper deals with set-valued equilibrium problems under conditions of pseudo-monotonicity. Concepts such as strict quasi-convexity, hemicontinuity and pseudo-monotonicity for extended real set-valued mappings are introduced and applied to obtain results on the existence of solutions of set-valued equilibrium problems generalizing those in the literature in the pseudo-monotone case. Applications to Browder variational inclusions under weakened conditions are given. In particular, it is shown that the upper semicontinuity from line segments of the involved pseudo-monotone set-valued operator is not needed in the whole space when solving Browder variational inclusions.

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Acknowledgements

The authors thank both the anonymous referee and the Editor-in-Chief for their careful reading of our paper and for their remarks and comments, which have considerably improved the initial version of this work.V.D. Rădulescu acknowledges the support through a grant of the Romanian 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, Médéa, Algeria

    Boualem Alleche

  2. Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059, Kraków, Poland

    Vicenţiu D. Rădulescu

  3. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Vicenţiu D. Rădulescu

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  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 in the pseudo-monotone case and applications to Browder variational inclusions. Optim Lett 12, 1789–1810 (2018). https://doi.org/10.1007/s11590-018-1233-2

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  • DOI: https://doi.org/10.1007/s11590-018-1233-2

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