Variational convergence of a new proximal algorithm for nonlinear general \(A\)-monotone operator equation systems in Banach spaces. (English) Zbl 1188.49013
Summary: The purpose of this paper is to introduce the notion of general \(A\)-monotone operators in Banach spaces and a new proximal mapping associated with 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.
Keywords:
general \(A\)-monotone operator; new proximal algorithm; nonlinear operator equation system with relaxed cocoercive operator; proximal mapping technique; existence and variational convergenceReferences:
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