Existence of solutions for generalized mixed variational inequalities in reflexive Banach spaces

Volume 9, Issue 5, pp 3299--3309 http://dx.doi.org/10.22436/jnsa.009.05.116

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Authors

Zhong-Bao Wang - Department of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 611756, P. R. China. Zi-Li Chen - Department of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 611756, P. R. China.

Abstract

This paper is devoted to the solvability of generalized mixed variational inequalities in reflexive Banach spaces. We prove the existence of solutions of the generalized mixed variational inequalities for f- quasimonotone set-valued mappings without any assumption on bounded values. Furthermore, we give some conditions that guarantee the existence of solutions of the generalized mixed variational inequalities over unbounded closed convex subsets. Our results extend and improve some recent results from the literature.

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Keywords

• Generalized mixed variational inequality
• reflexive Banach space
• existence
• f-quasimonotonicity.

MSC

•  49J40
•  47H10
•  47H17.

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