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Existence of solutions and convergence of a multistep iterative algorithm for a system of variational inclusions with \((H,\eta )\)-accretive operators. (English) Zbl 1155.47313

Summary: We introduce and study a new system of variational inclusions with \((H,\eta )\)-accretive operators, which contains variational inequalities, variational inclusions, systems of variational inequalities, and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the \((H,\eta )\)-accretive operators, we prove the existence and uniqueness of solutions and the convergence of a new multistep iterative algorithm for this system of variational inclusions in real \(q\)-uniformly smooth Banach spaces. The results in this paper unify, extend, and improve some known results in the literature.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J40 Variational inequalities
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