Algorithms for solutions of extended general mixed variational inequalities and fixed points

详细信息    查看全文

• 作者：Javad Balooee (1)
  Yeol Je Cho (2)
  
• 关键词：Variational inequalities ; Nearly uniformly Lipschitzian mappings ; Fixed point problems ; Resolvent operator ; Dynamical systems ; Convergence ; Primary 47H05 ; Secondary 47J20 ; 49J40 ; 90C33
• 刊名：Optimization Letters
• 出版年：2013
• 出版时间：December 2013
• 年：2013
• 卷：7
• 期：8
• 页码：1929-1955
• 全文大小：
• 作者单位：Javad Balooee (1)
  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：1862-4480

文摘

In this paper, we introduce and study a new class of extended general nonlinear mixed variational inequalities and a new class of extended general resolvent equations and establish the equivalence between the extended general nonlinear mixed variational inequalities and implicit fixed point problems as well as the extended general resolvent equations. Then by using this equivalent formulation, we discuss the existence and uniqueness of solution of the problem of extended general nonlinear mixed variational inequalities. Applying the aforesaid equivalent alternative formulation and a nearly uniformly Lipschitzian mapping S, we construct some new resolvent iterative algorithms for finding an element of set of the fixed points of nearly uniformly Lipschitzian mapping S which is the unique solution of the problem of extended general nonlinear mixed variational inequalities. We study convergence analysis of the suggested iterative schemes under some suitable conditions. We also suggest and analyze a class of extended general resolvent dynamical systems associated with the extended general nonlinear mixed variational inequalities and show that the trajectory of the solution of the extended general resolvent dynamical system converges globally exponentially to the unique solution of the extended general nonlinear mixed variational inequalities. The results presented in this paper extend and improve some known results in the literature.