Stability and convergence analysis for a new system of implicit variational-like inclusions based on variational convergence of generalized monotone operators

Abstract

A new system of nonlinear implicit variational-like inclusions is introduced. Using Lipschitz continuity of the generalized resolvent operator associated with a general H-maximal m-relaxed ?-monotone operator, existence and uniqueness of the solution of this new variational inclusions system via relaxed cocoercive mappings is proved. Moreover, a type of variational convergence of operators for general H-maximal m-relaxed ?-monotone operators is established and so by applying this result, stability and convergence analysis for a perturbed three step iterative algorithm are given.