Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces

Abstract

The purpose of this paper is to investigate thenonemptiness and boundedness of solution set for a generalized mixedvariational inequality problem with strict feasibility in reflexiveBanach spaces. We introduce a concept of strict feasibility for thegeneralized mixed variational inequality problem which includes theexisting concepts of strict feasibility introduced for variationalinequalities and complementarity problems. By using a degree theorydeveloped in Wang and Huang [28], we prove that the monotonegeneralized mixed variational inequality has a nonempty boundedsolution set if and only if it is strictly feasible. The resultspresented in this paper generalize and extend some known results in[8, 23].