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Existence of Solutions and Convergence of a Multistep Iterative Algorithm for a System of Variational Inclusions with -Accretive Operators

Abstract

We introduce and study a new system of variational inclusions with -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 -accretive operators, we prove the existence and uniqueness of solution and the convergence of a new multistep iterative algorithm for this system of variational inclusions in real -uniformly smooth Banach spaces. The results in this paper unify, extend, and improve some known results in the literature.

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Peng, JW., Zhu, DL. & Zheng, XP. Existence of Solutions and Convergence of a Multistep Iterative Algorithm for a System of Variational Inclusions with -Accretive Operators. Fixed Point Theory Appl 2007, 093678 (2007). https://doi.org/10.1155/2007/93678

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