Vector Implicit Mixed Quasi Complementarity Problems

摘要

In this paper, we introduce and study a new class of vector implicit mixed quasi complementarity problem and the corresponding vector implicit mixed quasi variational inequality problem in the setting of topological vector space. By using modified KKM mapping theorem, we derive existence of solutions of vector implicit mixed quasi variational inequalities and vector implicit mixed quasi complementarity problems. Under certain conditions their equivalency is discussed, which is the main motivation of this paper.