- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 A variant of the generalized vector variational inequality with operator solutions Commun. Korean Math. Soc. 2006 Vol. 21, No. 4, 665-673 Published online December 1, 2006 Sangho Kum Chungbuk National University Abstract : In a recent paper, Domokos and Kolumb\'an [2] gave an interesting interpretation of variational inequalities (VI) and vector variational inequalities (VVI) in Banach space settings in terms of variational inequalities with operator solutions (in short, OVVI). Inspired by their work, in a former paper [4], we proposed the scheme of generalized vector variational inequality with operator solutions (in short, GOVVI) which extends (OVVI) into a multi-valued case. In this note, we further develop the previous work [4]. A more general pseudomonotone operator is treated. We present a result on the existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [8] within the framework of (GOVVI) by exploiting some techniques on (GOVVI) or (GVVI) in [4]. Keywords : vector variational inequality, weakly $C$-pseudemonotone operator, generalized hemicontinuity, Fan-Browder fixed point theorem MSC numbers : 47J20, 49J40 Downloads: Full-text PDF