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General system of \(A\)-monotone nonlinear variational inclusions problems with applications. (English) Zbl 1185.47073

Summary: We introduce and study a new system of nonlinear variational inclusions involving a combination of \(A\)-monotone operators and relaxed cocoercive mappings. By using the resolvent technique of the \(A\)-monotone operators, we prove the existence and uniqueness of solution and the convergence of a new multistep iterative algorithm for this system of variational inclusions. The results in this paper unify, extend, and improve some known results in literature.

MSC:

47J22 Variational and other types of inclusions
47J25 Iterative procedures involving nonlinear operators
49J40 Variational inequalities
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References:

[1] Fang YP, Huang NJ: -monotone operators and system of variational inclusions.Communications on Applied Nonlinear Analysis 2004,11(1):93-101. · Zbl 1040.49007
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