Auxiliary problem principle extended to variational inequalities
Journal of Optimization Theory and Applications
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
General algorithm for variational inequalities
Journal of Optimization Theory and Applications
Some aspects of variational inequalities
Journal of Computational and Applied Mathematics
Nonconvex functions and variational inequalities
Journal of Optimization Theory and Applications
Perturbed proximal point algorithms for general quasi-variational-like inclusions
Journal of Computational and Applied Mathematics - Fixed point theory with applications in nonlinear analysis
Interative schemes for solving mixed variational-like inequalites1,2
Journal of Optimization Theory and Applications
Journal of Computational and Applied Mathematics
Existence of generalized variational inequalities
Operations Research Letters
Iterative algorithm for finding approximate solutions of mixed quasi-variational-like inclusions
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
Existence and algorithms for bilevel generalized mixed equilibrium problems in Banach spaces
Journal of Global Optimization
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In this paper, we study a class of mixed quasi-variational-like inclusion with a bifunction in reflexive Banach spaces. By applying a minimax inequality due to the first author, some existence and uniqueness theorems of solutions for the mixed quasi-variational-like inclusions are proved. Next, by applying the auxiliary variational inequality technique, we suggest an iterative algorithm to compute the approximate solutions of the mixed quasi-variational-like inclusions. The convergence criteria of the algorithm is studied under quite mild conditions. Our results represent improvement and generalization of the previously known results in literature.