A new class of variational inclusions with <i>B</i>-monotone operators in Banach spaces

作     者：Luo, Xue-ping Huang, Nan-jing 

作者机构：Sichuan Univ Dept Math Chengdu 610064 Sichuan Peoples R China 

出 版 物：《JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS》 (计算与应用数学杂志)

年 卷 期：2010年第233卷第8期

页      面：1888-1896页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：NSFC National Natural Science Foundation of China Higher Education 

主　　题：B-monotone operator Proximal mapping Iterative algorithm Variational inclusion Convergence 

摘      要：In this paper, we introduce and study a new class of variational inclusions in Banach spaces. For solving such class of variational inclusions, we introduce a new notion of B-monotone operator and prove the Lipschitz continuity of the proximal mapping associated with the B-monotone operator. By using the proximal mapping, an iterative algorithm for solving such class of variational inclusions is constructed in Banach spaces. Under some suitable conditions, we prove the convergence of iterative sequence generated by the algorithm. (C) 2009 Elsevier B.V. All rights reserved.