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

Abstract

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