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Generalized vector implicit quasi complementarity problems. (English) Zbl 1242.90261

Summary: We introduce and study a generalized class of vector implicit quasi complementarity problem and the corresponding vector implicit quasi variational inequality problem. By using Fan-KKM theorem, we derive existence of solutions of generalized vector implicit quasi variational inequalities without any monotonicity assumption and establish the equivalence between those problems in Banach spaces.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
49J40 Variational inequalities
47H10 Fixed-point theorems
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