Variational convergence of a new proximal algorithm for nonlinear general AA-monotone operator equation systems in Banach spaces

The purpose of this paper is to introduce the notion of general AA-monotone operators in Banach spaces and the new proximal mapping associated with the general AA-monotone operators. By using Alber’s inequalities and the new proximal mapping technique, the variational convergence of a new proximal algorithm for nonlinear general AA-monotone operator equation systems with relaxed cocoercive operators in Banach spaces is introduced and studied. Our results improve and generalize the corresponding results of recent works.