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Vector Quasi-Equilibrium Problems for the Sum of Two Multivalued Mappings

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Abstract

In this paper, we study vector quasi-equilibrium problems for the sum of two multivalued bifunctions. The assumptions are required separately on each of these bifunctions. Sufficient conditions for the existence of solutions of such problems are shown in the setting of topological vector spaces. The results in this paper unify, improve and extend some well-known existence theorems from the literature.

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Acknowledgments

The research of the first two authors was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, Project Number PN-II-ID-PCE-2011-3-0024. The third author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2014.17. The work of the third author on this paper is dedicated to Prof. Pham Huu Sach, in celebration of his 75th birthday. The authors wish to thank the anonymous referees for their useful comments, which helped them to improve the presentation of the paper.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu, 400084, Cluj-Napoca, Romania

    Gábor Kassay

  2. Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului, 400114, Cluj-Napoca, Romania

    Mihaela Miholca

  3. Department of Mathematics, University of Transport and Communications, 3 Cau Giay Street, Hanoi, Vietnam

    Nguyen The Vinh

Authors
  1. Gábor Kassay
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  2. Mihaela Miholca
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  3. Nguyen The Vinh
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Correspondence to Gábor Kassay.

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Communicated by Patrice Marcotte.

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Kassay, G., Miholca, M. & Vinh, N.T. Vector Quasi-Equilibrium Problems for the Sum of Two Multivalued Mappings. J Optim Theory Appl 169, 424–442 (2016). https://doi.org/10.1007/s10957-016-0919-9

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  • DOI: https://doi.org/10.1007/s10957-016-0919-9

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