Existence of Solutions and Convergence of a Multistep Iterative Algorithm for a System of Variational Inclusions with "Equation missing" -Accretive Operators
Jian-Wen Peng, Daoli Zhu, Xiaoping Zheng · Fixed Point Theory and Applications · 2007
Abstract We introduce and study a new system of variational inclusions with "Equation missing"-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 "Equation missing"-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 "Equation missing"-uniformly smooth Banach spaces. The results in this paper unify, extend, and improve some known results in the literature.