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
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