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

Authors:
Jian-Wen Peng
Affiliations:
College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, People's Republic of China 400047
Venue:
Journal of Global Optimization
Year:
2007

Citing 13
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Abstract

In this paper, we introduce and study a new system ofvariational inclusions with (A, η,m)-accretive operators which contains variationalinequalities, variational inclusions, systems of variationalinequalities and systems of variational inclusions in theliterature as special cases. By using the resolvent technique forthe (A, η, m)-accretive operators, weprove the existence and uniqueness of solution and the convergenceof a new multi-step iterative algorithm for this system ofvariational inclusions in real q-uniformly smooth Banachspaces. The results in this paper unifies, extends and improvessome known results in the literature.