Quasi-Strict Feasibility of Generalized Mixed Variational Inequalities in Reflexive Banach Spaces

Abstract

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).