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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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
Keywords
- Ky Fan inequality
- Browder–Fan mapping
- Vector quasi-equilibrium problem
- Upper (lower) C-mapping
- C-upper (lower) semicontinuous
- Multivalued mapping
- Generalized C-essentially quasimonotone