Quasi-Strict Feasibility of Generalized Mixed Variational Inequalities in Reflexive Banach Spaces
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In this paper, quasi-strict feasibility of a generalized mixed variational inequality as a new notation is introduced, which is weaker than its strict feasibility and recovers the existing concept of strict feasibility for a generalized variational inequality. By using the equivalent characterization of the nonemptiness and boundedness of the solution set for the generalized mixed variational inequality, it is proved that quasi-strict feasibility is a sufficient condition for the generalized mixed variational inequality with a f-pseudomonotone and upper hemicontinuous mapping to have a nonempty and bounded solution set in reflexive Banach spaces. Our results generalize and extend some known results in Zhong and Huang (J Optim Theory Appl 152(3):696–709, 2012).
KeywordsQuasi-strict feasibility Generalized mixed variational inequality f-pseudomonotone
Mathematics Subject Classification47H05 49J40 49J53
The work was supported by National Natural Science Foundation of China (Grant 11701480), Fundamental Research Funds for the Central Universities, Southwest University for Nationalities (Grant 2018HQZZ23), Key Projects of the Education Department of Sichuan Province (Grant 18ZA0511), Innovation Team Funds of Southwest University for Nationalities (Grant 14CXTD03), Innovative Research Team of the Education Department of Sichuan Province (Grant 15TD0050) and Sichuan Youth Science and Technology Innovation Research Team (Grant 2017TD0028).