A new explicit triple hierarchical problem over the set of fixed points and generalized mixed equilibrium problems

详细信息    查看全文

• 作者：Thanyarat Jitpeera (1)
  Poom Kumam (1)
  
• 关键词：nonexpansive mapping ; strong converge ; variational inequality ; projection ; hierarchical problem ; Hilbert space
• 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：261KB
• 参考文献：1. Blum E, Oettli W: From optimization and variational inequalities to equilibrium problems. / Math Student 1994, 63:123鈥?45.
  2. Hartman P, Stampacchia G: On some nonlinear elliptic differential functional equations. / Acta Math 1966, 115:271鈥?10. CrossRef
  3. Cianciaruso F, Marino G, Muglia L, Yao Y: On a two-step algorithm for hierarchical fixed point problems and variational inequalities. / J Inequal Appl 2009, 2009:13. Article ID 208692 CrossRef
  4. Yao JC, Chadli O: / Pseudomonotone complementarity problems and variational inequalities. Edited by: Crouzeix JP, Haddjissas N, Schaible S. Handbook of Generalized Convexity and Monotonicity; 2005:501鈥?58.
  5. Kirk WA: Fixed point theorem for mappings which do not increase distance. / Am Math Monthly 1965, 72:1004鈥?006. CrossRef
  6. Yao Y, Liou Y-C, Chen C-P: Hierarchical convergence of a double-net algorithm for equilibrium problems and variational inequality problems. / Fixed Point Theory Appl 2010, 2010:16. Article ID 642584 CrossRef
  7. Marino G, Xu H-K: Explicit hierarchical fixed point approach to variational inequalities. / J Optim Theory Appl 2011, 149:61鈥?8. doi:10.1007/s10957鈥?10鈥?775鈥? CrossRef
  8. Jitpeera T, Kumam P: Hybrid algorithms for minimization problems over the solutions of generalized mixed equilibrium and variational inclusion problems. / Mathematical Problems in Engineering 2011., 25: Article ID 648617 doi:10.1155/2011/648617
  9. Browder FE: Nonlinear operators and nonlinear equations of evolution in Banach spaces. / Proc Symp Pure Math 1976, 18:78鈥?1.
  10. Peng JW, Yao JC: A new hybrid-extragradient method for generalized mixed equilibrium problems and fixed point problems and variational inequality problems. / Taiwanese J Math 2008,12(6):1401鈥?432.
  11. Xu HK: Iterative algorithms for nonlinear operators. / J Lond Math Soc 2002, 66:240鈥?56. CrossRef
  
• 作者单位：Thanyarat Jitpeera (1)
  Poom Kumam (1)
  
  1. Department of Mathematics, Faculty of Science, King Mongkut鈥檚 University of Technology Thonburi (KMUTT), Bangmod, Thrungkru, Bangkok, 10140, Thailand
  
• ISSN：1029-242X

文摘

In this article, we introduce and consider the triple hierarchical over the fixed point set of a nonexpansive mapping and the generalized mixed equilibrium problem set of an inverse-strongly monotone napping. The strong convergence of the algorithm is proved under some mild conditions. Our results generalize and improve the results of Marino and Xu and some authors. Mathematics Subject Classification (2000): 47H09; 47H10; 47J20; 49J40; 65J15.