Iterative Methods for Solving a System of Variational Inclusions Involving $(H,\eta)$-Monotone Operators in Banach Spaces
Received:January 29, 2007  Revised:July 13, 2007
Key Word: $q$-uniformly smooth space   $(H, \eta)$-monotone operator   Resolvent operator technique   system of variational inclusion   iterative algorithm.
Fund ProjectL:the Key Project of Chinese Ministry of Education (No.207104); the Natural Science Foundation of Hebei Province (No.A2006000941).
 Author Name Affiliation LOU Jian Computer Center, Hebei University, Hebei 071002, China HE Xin Feng College of Mathematics and Computers, Hebei University, Hebei 071002, China HE Zhen College of Mathematics and Computers, Hebei University, Hebei 071002, China
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In this paper, we introduce and study a new system of variational inclusions involving $(H, \eta)$-monotone operators in Banach space. Using the resolvent operator associated with $(H, \eta)$- monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the iterative sequence generated by the algorithm.