Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces
Computers & Mathematics with Applications
Existence of generalized variational inequalities
Operations Research Letters
Computers & Mathematics with Applications
Existence and algorithms for bilevel generalized mixed equilibrium problems in Banach spaces
Journal of Global Optimization
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In this paper, we introduce and study a new system of generalized set-valued mixed variational-like inequality problems (SGSMVLIP) and its related auxiliary problems in reflexive Banach spaces. The auxiliary principle technique is applied to study the existence and an iterative algorithm of solutions for the system of generalized set-valued mixed variational-like inequality problems. At first, the existence and uniqueness of solutions of the auxiliary problems for (SGSMVLIP) is shown. Next, an iterative algorithm for solving (SGSMVLIP) is constructed by using the existence and uniqueness result. Finally, we prove the existence of solutions of (SGSMVLIP) and discuss the convergence analysis of the algorithm. These results improve, unify and generalize many corresponding known results given in the literature.