Iterative algorithms for a new class of extended general nonconvex set-valued variational inequalities

作     者：Alimohammady, M. Balooee, J. Cho, Y. J. Roohi, M. 

作者机构：Gyeongsang Natl Univ Dept Math Educ Chinju 660701 South Korea Gyeongsang Natl Univ RINS Chinju 660701 South Korea Univ Mazandaran Dept Math Fac Basic Sci Babol Sar 474161468 Iran 

出 版 物：《NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS》 (非线性分析)

年 卷 期：2010年第73卷第12期

页      面：3907-3923页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Variational inequalities Wiener-Hopf inclusions Iterative algorithm Monotone operators Prox-regularity Convergence analysis 

摘      要：Some new classes of extended general nonconvex set-valued variational inequalities and the extended general Wiener-Hopf inclusions are introduced. By the projection technique, equivalence between the extended general nonconvex set-valued variational inequalities and the fixed point problems as well as the extended general nonconvex Wiener-Hopf inclusions is proved. Then by using this equivalent formulation, we discuss the existence of solutions of the extended general nonconvex set-valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the extended general nonconvex set-valued variational inequalities. We also verify that the approximate solutions obtained by our algorithms converge to the solutions of the extended general nonconvex set-valued variational inequalities. The results presented in this paper extend and improve some known results from the literature. (C) 2010 Elsevier Ltd. All rights reserved.