Perturbed projection and iterative algorithms for a system of general regularized nonconvex variational inequalities
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- 作者：Javad Balooee (1)
Yeol Je Cho (2) - 关键词：variational inequalities ; nearly uniformly Lipschitzian mapping ; prox ; regularity ; fixed point problem ; convergence analysis
- 刊名：Journal of Inequalities and Applications
- 出版年：2012
- 出版时间：December 2012
- 年：2012
- 卷：2012
- 期：1
- 全文大小：358KB
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Yeol Je Cho (2)
1. Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
2. Department of Mathematics Education and RINS, Gyeongsang National University, Chinju, 660-701, Korea - ISSN：1029-242X
文摘
The purpose of this paper is to introduce a new system of general nonlinear regularized nonconvex variational inequalities and verify the equivalence between the proposed system and fixed point problems. By using the equivalent formulation, the existence and uniqueness theorems for solutions of the system are established. Applying two nearly uniformly Lipschitzian mappings S 1 and S 2 and using the equivalent alternative formulation, we suggest and analyze a new perturbed p-step projection iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping which is the unique solution of the system of general nonlinear regularized nonconvex variational inequalities. We also discuss the convergence analysis of the proposed iterative algorithm under some suitable conditions. MSC : Primary 47H05; Secondary 47J20, 49J40, 90C33.