Mixed vector $FQ$-implicit variational inequality with local non-positivity
Commun. Korean Math. Soc. 2009 Vol. 24, No. 3, 425-432
https://doi.org/10.4134/CKMS.2009.24.3.425
Printed September 1, 2009
Byung-Soo Lee
Kyungsung University
Abstract : This paper introduces a local non-positivity of two set-valued mappings $(F,Q)$ and considers the existences and properties of solutions for set-valued mixed vector $FQ$-implicit variational inequality problems and set-valued mixed vector $FQ$-complementarity problems in the neighborhood of a point belonging to an underlined domain $K$ of the set-valued mappings, where the neighborhood is contained in $K$. This paper generalizes and extends many results in [1, 3-7].
Keywords : mixed vector $FQ$-implicit complementarity problem, mixed vector $FQ$-implicit variational inequality problem, positively homogeneous mapping, convex cone, upper semicontinuity, lower semicontinuity, locally non-positive
MSC numbers : 90C33, 49J40
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