Abstract
In this paper we study the solvability of the generalized vector variational inequality problem, the GVVI problem, with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVVIs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVVI problems without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also the extension and improvement of some recent results in the literature.
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Dedicated to Professor Franco Giannessi for his 75th Birthday.
This research was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai.
This research was partially supported by a grant from the National Science Council.
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Ceng, LC., Huang, S. Existence theorems for generalized vector variational inequalities with a variable ordering relation. J Glob Optim 46, 521–535 (2010). https://doi.org/10.1007/s10898-009-9436-9
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DOI: https://doi.org/10.1007/s10898-009-9436-9
Keywords
- Generalized vector variational inequality
- Variable ordering relation
- Cone mapping
- KKM-Fan theorem
- Brouwer fixed point theorem
- Monotonicity
- Complete continuity