Abstract
The purpose of this paper is to introduce the notion of general A -monotone operators in Banach spaces and the new proximal mapping associated with the general A -monotone operators. By using Alber’s inequalities and the new proximal mapping technique, the variational convergence of a new proximal algorithm for nonlinear general A -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.
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