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The Wiener-Hopf Equation Technique for Solving General Nonlinear Regularized Nonconvex Variational Inequalities
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  • 作者：Javad Balooee (1)
    Yeol Je Cho (2)
    Mee Kwang Kang (3)
  • 关键词：variational inequalities ; fixed point problems ; prox ; regularity ; nearly uniformly Lipschitzian mappings ; p ; step projection iterative algorithms ; extended general nonconvex Wiener ; Hopf equations ; convergence analysis
  • 刊名：Fixed Point Theory and Applications
  • 出版年：2011
  • 出版时间：December 2011
  • 年：2011
  • 卷：2011
  • 期：1
  • 全文大小：414KB
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  • 作者单位：Javad Balooee (1)
    Yeol Je Cho (2)
    Mee Kwang Kang (3)

    1. Department of Mathematics, Sari Branch Islamic Azad University, Sari, Iran
    2. Department of Mathematics Education and the RINS Gyeongsang National University, Chinju, 660-701, Korea
    3. Department of Mathematics, Dongeui University, Pusan, 614-714, Korea
  • ISSN：1687-1812
文摘
In this paper, we introduce and study some new classes of extended general nonlinear regularized non-convex variational inequalities and the extended general nonconvex Wiener-Hopf equations, and by the projection operator technique, we establish the equivalence between the extended general nonlinear regularized nonconvex variational inequalities and the fixed point problems as well as the extended general nonconvex Wiener-Hopf equations. Then by using this equivalent formulation, we discuss the existence and uniqueness of solution of the problem of extended general nonlinear regularized nonconvex variational inequalities. We apply the equivalent alternative formulation and a nearly uniformly Lipschitzian mapping S for constructing some new p-step projection iterative algorithms with mixed errors for finding an element of set of the fixed points of nearly uniformly Lipschitzian mapping S which is unique solution of the problem of extended general nonlinear regularized nonconvex variational inequalities. We also consider the convergence analysis of the suggested iterative schemes under some suitable conditions. Mathematics Subject Classification (2010) Primary 47H05; Secondary 47J20, 49J40

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