Existence of solutions for generalized nonlinear mixed variational‐like inequalities in Banach spaces
Yali Zhao, Zun-Quan Xia, Zeqing Liu, Shin Min Kang · International Journal of Mathematics and Mathematical Sciences · 2006
We introduce and study a new class of generalized nonlinear mixed variational‐like inequalities in reflexive Banach spaces. By applying Ding′s technique we prove several existence and uniqueness theorems of solutions for the generalized nonlinear mixed variational‐like inequality, extend the auxiliary problem technique to suggest and analyze an iterative method to compute the approximate solutions of the generalized nonlinear mixed variational‐like inequality, and establish the convergence criteria of the iterative method. The results presented in this paper improve, extend, and unify many known results in this area.