Algorithms For Completely Generalized Mixed Implicit Quasi-variational-like Inclusions And Mixed Variational Inequality

In recent years, efficient iterative algorithms to compute approximate solutions of variational inequality have been studied by Ding, Hong-Kun Xu, Noor and other authors at home and abroad. They also analyze the convergence of the iterative algorithms. The main purpose of this thesis is to make discussion a new class of completely generalized mixed implicit quasi-variational-like inclusions and mixed variational inequality by applying the auxiliary variational inequality technique and CQ method.The thesis is composed of three sections. First, we show the real background of the problems we study and the main works that have been studied by many authors. We also introduce some basic definition and the main results in this article. Second, predictor-corrector iterative algorithm is suggested for solving completely generalized mixed implicit quasi-variational-like inclusion problem by applying the auxiliary variational inequality technique. By introducing two concepts of g-partially relaxed reversalη-strongly monotonicity of single-valued mappings and g-partially relaxed stronglyηmonotonicity with respect to h of set-valued mappings, we prove the convergence of the iterative sequence generated by suggested iterative algorithm. In the last section,CQ iterative algorithm is suggested for solving mixed variational inequality problem. Then we prove the convergence of the iterative sequence generated by the CQ method.In all, the results presented in the paper generalize and unify known results in recent literatures.