## Vector mixed quasi complementarity problems in Banach spaces.(English)Zbl 1255.90115

Summary: We introduce a new class of set-valued vector implicit quasi complementarity problems with corresponding set-valued implicit quasi variational inequality problems. By means of the Fan-KKM theorem, we investigate the nonemptiness and compactness of solution sets of these problems. Our work generalizes and improves some results appeared recently in the literature.

### MSC:

 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 90C31 Sensitivity, stability, parametric optimization 49J40 Variational inequalities

### Keywords:

convex cone; quasi complementarity problem; process mapping
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### References:

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