Abstract
We introduce and study a new class of general nonlinear implicit variational inequalities, which includes several classes of variational inequalities and variational inclusions as special cases. By applying the resolvent operator technique and fixed point theorem, we suggest a new perturbed three-step iterative algorithm with errors for solving the class of variational inequalities. Several existence and uniqueness results of solutions for the general nonlinear implicit variational inequalities, and convergence and stability results of the sequence generated by the algorithm are obtained. The results presented in this paper extend, improve, and unify a host of results in recent literatures.
Highlights
In recent years, various extensions and generalizations of the variational inequalities have been considered and studied
It is well known that one of the most interesting and important problems in the variational inequality theory is the development of an efficient iterative algorithm to compute approximate solutions of various variational inequalities and inclusions
In 2003, Fang and Huang 7 introduced the definitions of H-monotone operator and its resolvent operator, established the Lipschitz continuity of the resolvent operator, constructed an iterative
Summary
Various extensions and generalizations of the variational inequalities have been considered and studied. Several existence and uniqueness results of solutions for the general nonlinear implicit variational inequalities involving H-monotone, strongly monotone, relaxed monotone, relaxed Lipschitz and generalized pseudocontractive operators, and convergence and stability results of the perturbed three-step iterative process with errors are given.
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