Auxiliary principle for completely generalized set-valued strongly nonlinear implicit variational inequalities

摘要

In this paper, we introduce and study a new class of variational inequalities, which is called the completely generalized set-valued strongly nonlinear implicit variational inequality. Using the auxiliary principle technique with two parameters, we establish the existence theorems of solutions for the class of completely generalized set-valued strongly nonlinear implicit variational inequalities dealing with the strongly monotone, relaxed Lipschitz and relaxed monotone mappings, respectively, construct the iterative algorithm and show the convergence results of iterative sequences generalized by the algorithm. Our results extend, improve and unify the results due to Noor, Yao, and Huang et al.