An iterative algorithm for fixed point problem and convex minimization problem with applications

详细信息    查看全文

• 作者：Gang Cai ; Yekini Shehu
• 关键词：47H06 ; 47H09 ; 47J05 ; 47J25 ; convex minimization problem ; k ; strictly pseudo contractive mapping ; strong convergence ; Hilbert spaces
• 刊名：Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,243 KB
• 参考文献：1. Browder, FE, Petryshyn, WV: Construction of fixed points of nonlinear mappings in Hilbert space. J. Math. Anal. Appl. 20, 197-228 (1967) CrossRef
  2. Acedo, GL, Xu, H-K: Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal. 67, 2258-2271 (2007) CrossRef
  3. Ceng, LC, Al-Homidan, S, Ansari, QH, Yao, JC: An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings. J. Comput. Appl. Math. 223, 967-974 (2009) CrossRef
  4. Chidume, CE, Abbas, M, Ali, B: Convergence of the Mann iteration algorithm for a class of pseudo-contractive mappings. Appl. Math. Comput. 194, 1-6 (2007) CrossRef
  5. Cholamjiak, P, Suantai, S: Strong convergence for a countable family of strict pseudocontractions in / q-uniformly smooth Banach spaces. Comput. Math. Appl. 62, 787-796 (2011) CrossRef
  6. Hao, Y, Cho, SY: Some results on strictly pseudocontractive nonself mapping and equilibrium problems in Hilbert spaces. Abstr. Appl. Anal. 2012, Article ID 543040 (2012)
  7. Jaiboon, C, Kumam, P: Strong convergence theorems for solving equilibrium problems and fixed point problems of strictly pseudocontraction mappings by two hybrid projection methods. J. Comput. Appl. Math. 234(3), 722-732 (2010) CrossRef
  8. Jung, JS: Iterative methods for mixed equilibrium problems and pseudocontractive mappings. Fixed Point Theory Appl. 2012, Article ID 184 (2012) CrossRef
  9. Liu, Y: A general iterative method for equilibrium problems and strict pseudo-contractions in Hilbert spaces. Nonlinear Anal. 71, 4852-4861 (2009) CrossRef
  10. Marino, G, Xu, H-K: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl. 329(1), 336-346 (2007) CrossRef
  11. Qin, L-J, Wang, L: An iteration method for solving equilibrium problems, common fixed point problems of pseudocontractive mappings of Browder-Petryshyn type in Hilbert spaces. Int. Math. Forum 6(2), 63-74 (2011)
  12. Shehu, Y: Iterative methods for family of strictly pseudocontractive mappings and system of generalized mixed equilibrium problems and variational inequality problems. Fixed Point Theory Appl. 2011, Article ID 852789 (2011) CrossRef
  13. Zhou, HY: Convergence theorems of fixed points for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal. 69(2), 456-462 (2008) CrossRef
  14. Bertsekas, DP, Gafni, EM: Projection methods for variational inequalities with applications to the traffic assignment problem. Math. Program. Stud. 17, 139-159 (1982) CrossRef
  15. Han, D, Lo, HK: Solving non-additive traffic assignment problems: a descent method for co-coercive variational inequalities. Eur. J. Oper. Res. 159, 529-544 (2004) CrossRef
  16. Xu, HK: Averaged mappings and the gradient-projection algorithm. J. O
• 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
• 出版者：Springer International Publishing
• ISSN：1687-1812

文摘

In this paper we prove the strong convergence of an iterative sequence for finding a common element of the fixed points set of a strictly pseudocontractive mapping and the solution set of the constrained convex minimization problem for a convex and continuously Fréchet differentiable functional in a real Hilbert space. We apply our result to solving the split feasibility problem and the convexly constrained linear inverse problem involving the fixed point problem for a strictly pseudocontractive mapping in a real Hilbert space.