Nonlinear Set-Valued Variational-Like Inclusions via Relaxed Cocoercive Operators with Perturbed Iterative Algorithm

Abstract

In this paper, a new system of nonlinear set-valued variational-like inclusions is introduced. Using Lipschitz continuity of the generalized resolvent operator associated with general H-maximal m-relaxed ?-monotone operators, existence and uniqueness of the solution of this new variational inclusion system via relaxed cocoercive operators is proved. Finally, a three-step perturbed iterative algorithm and its convergence analysis are given.