# MIXED VECTOR FQ-IMPLICIT VARIATIONAL INEQUALITIES WITH FQ-COMPLEMENTARITY PROBLEMS

Lee, Byung-Soo

• Accepted : 2009.03.18
• Published : 2009.06.25
• 30 6

#### Abstract

This paper introduces new mixed vector FQ-implicit variational inequality problems and corresponding mixed vector FQ-implicit complementarity problems for set-valued mappings, and studies the equivalence between them under certain assumptions in Banach spaces. It also derives some new existence theorems of solutions for them with examples under suitable assumptions without monotonicity. This paper generalizes and extends many results in [8, 10, 19-22].

#### Keywords

Mixed vector FQ-implicit complementarity problem;Mixed vector FQ-implicit variational inequality problem;KKM-mapping;Fan-KKM Theorem;Positively homogeneous mapping;Convex cone;Upper semicontinuity;Lower semicontinuity

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