Existence of Solutions and Convergence of a Multistep Iterative Algorithm for a System of Variational Inclusions with <inline-formula><graphic file="1687-1812-2007-093678-i1.gif"/></inline-formula>-Accretive Operators

• Main Authors: Zhu Dao-Li, Zheng Xiao-Ping, Peng Jian-Wen
• Format: Article
• Language: English
• Published: SpringerOpen 2007-01-01
• Series: Fixed Point Theory and Applications
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2007/093678

<p/> <p>We introduce and study a new system of variational inclusions with <inline-formula><graphic file="1687-1812-2007-093678-i2.gif"/></inline-formula>-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 <inline-formula><graphic file="1687-1812-2007-093678-i3.gif"/></inline-formula>-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 <inline-formula><graphic file="1687-1812-2007-093678-i4.gif"/></inline-formula>-uniformly smooth Banach spaces. The results in this paper unify, extend, and improve some known results in the literature.</p>