Peng, Jian-Wen; Zhao, Lai-Jun General system of \(A\)-monotone nonlinear variational inclusions problems with applications. (English) Zbl 1185.47073 J. Inequal. Appl. 2009, Article ID 364615, 13 p. (2009). 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. Cited in 4 Documents MSC: 47J22 Variational and other types of inclusions 47J25 Iterative procedures involving nonlinear operators 49J40 Variational inequalities Keywords:nonlinear variational inclusions; relaxed cocoercive mappings; resolvent technique; \(A\)-monotone operators; existence; uniqueness; multistep iterative algorithm PDFBibTeX XMLCite \textit{J.-W. Peng} and \textit{L.-J. Zhao}, J. Inequal. Appl. 2009, Article ID 364615, 13 p. (2009; Zbl 1185.47073) Full Text: DOI EuDML 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.