Existence of solutions of generalized vector variational-type inequalities with set-valued mappings

Authors:
Si-Jia Jiang;Li-Ping Pang;Jie Shen
Affiliations:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;School of Mathematics, Liaoning Normal University, Dalian 116029, China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

In this paper, we introduce a new class of generalized vector variational-type inequalities with set-valued mappings (GVVTI). First, the solvability of generalized vector variational-type inequalities without monotone assumption is considered in Banach spaces by using Brouwer's fixed point theorem. Second, by the introduction of the concepts of pseudomonotone, v-coercive and @h-hemicontinuous, the solvability of (GVVTI) is obtained with the assumption of @h-hemicontinuous and pseudomonotone.