Iterative Methods for Mixed Variational Inequalities and Nonexpansive Mappings
AI Yi-hong · Journal of Sichuan Normal University · 2012
In this paper,we introduce and study a new class of generalized mixed variational inequalities.The class of mixed variational inequalities includes many known variational inequality problems and complementarity problems as special cases.By using the generalized Wiener-Hopf equation technique,we suggest and analyze an iterative method for finding the common element of the set of fixed points of nonexpansive mappings and the set of solutions of the generalized mixed variational inequalities.The strong convergence of the suggested algorithm only requires the relaxed cocoercive and the Lipschitzian continuity of the mappings.Our results can be viewed as a novel and important extension and improvement of the previously known results.