Perturbed projection and iterative algorithms for a system of general regularized nonconvex variational inequalities

Abstract

The purpose of this paper is to introduce a new system of general nonlinear regularized nonconvex variational inequalities and verify the equivalence between the proposed system and fixed point problems. By using the equivalent formulation, the existence and uniqueness theorems for solutions of the system are established. Applying two nearly uniformly Lipschitzian mappings S 1 and S2 and using the equivalent alternative formulation, we suggest and analyze a new perturbed p-step projection iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q = (S1, S2) which is the unique solution of the system of general nonlinear regularized nonconvex variational inequalities. We also discuss the convergence analysis of the proposed iterative algorithm under some suitable conditions. © 2012 Balooee and Je Cho; licensee Springer.