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Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces

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  • The purpose of this paper is to investigate the nonemptiness and boundedness of solution set for a generalized mixed variational inequality problem with strict feasibility in reflexive Banach spaces. We introduce a concept of strict feasibility for the generalized mixed variational inequality problem which includes the existing concepts of strict feasibility introduced for variational inequalities and complementarity problems. By using a degree theory developed in Wang and Huang [28], we prove that the monotone generalized mixed variational inequality has a nonempty bounded solution set if and only if it is strictly feasible. The results presented in this paper generalize and extend some known results in [8, 23].
    Mathematics Subject Classification: Primary: 49J40; Secondary: 49J53.

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