ITERATIVE ALGORITHMS FOR SOLUTIONS OF GENERALIZED REGULARIZED NONCONVEX VARIATIONAL INEQUALITIES

Abstract

A new system of generalized nonlinear regularized nonconvex variational inequalities involving three different nonlinear operators is introduced and the equivalence between the aforesaid system and a fixed point problem is proved. Then by this equivalent formulation, the existence and uniqueness theorem for solution of the system of generalized nonlinear regularized nonconvex variational inequalities is established. Some new three-step projection iterative schemes for approximating the unique solution of the aforementioned system are constructed. The convergence analysis of the suggested iterative algorithms under some suitable conditions are also studied.