A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications

[摘要] A new system of generalized mixed quasivariational inclusions(for short, SGMQVI) with relaxed cocoercive operators, which develop some preexistingvariational inequalities, is introduced and investigated in Banach spaces. Next, the existence and uniqueness of solutions to the problem (SGMQVI) are established in real Banachspaces. From fixed point perspective, we propose some new iterative algorithms for solvingthe system of generalized mixed quasivariational inclusion problem (SGMQVI). Moreover,strong convergence theorems of these iterative sequences generated by the correspondingalgorithms are proved under suitable conditions. As an application, the strong convergencetheorem for a class of bilevel variational inequalities is derived in Hilbert space. The mainresults in this paper develop, improve, and unify some well-known results in the literature.

[学科分类] 应用数学