EXTENDED GENERAL VARIATIONAL INEQUALITY FOR RELAXED COCOERCIVE MAPPINGS IN HILBERT SPACES

Abstract

In this paper, we consider an extended general variational inequality with three nonlinear operators, more precisely, relaxed (α, r)-cocoercive mappings. Using the projection technique, we show that the extended general variational inequality is equivalent to the nonlinear projection equation. This alternative equivalent formulation is used to discuss the existence and convergence(or approximate solvability) of a solution of the extended general variational inequality under suitable conditions.