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The existence and uniqueness of solution and the convergence of a multi-step iterative algorithm for a system of variational inclusions with (A, η, m)-accretive operators

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Abstract

In this paper, we introduce and study a new system of variational inclusions with (A, η, m)-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 (A, η, m)-accretive operators, we prove the existence and uniqueness of solution and the convergence of a new multi-step iterative algorithm for this system of variational inclusions in real q-uniformly smooth Banach spaces. The results in this paper unifies, extends and improves some known results in the literature.

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  1. College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 400047, People’s Republic of China

    Jian-Wen Peng

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Peng, JW. The existence and uniqueness of solution and the convergence of a multi-step iterative algorithm for a system of variational inclusions with (A, η, m)-accretive operators. J Glob Optim 39, 441–457 (2007). https://doi.org/10.1007/s10898-007-9148-y

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  • DOI: https://doi.org/10.1007/s10898-007-9148-y

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