Strong convergence of an Ishikawa-type algorithm in spaces

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• 作者：Hafiz Fukhar-ud-din (1) (2)
  
• 关键词：asymptotically nonexpansive type map ; common fixed point ; Ishikawa ; type algorithm ; uniform equicontinuity ; strong convergence
• 刊名：Fixed Point Theory and Applications
• 出版年：2013
• 出版时间：December 2013
• 年：2013
• 卷：2013
• 期：1
• 全文大小：180 KB
• 参考文献：1. Kirk WA: Geodesic geometry and fixed point theory. In / Seminar of Mathematical Analysis. Univ. Sevilla Secr. Publ., Seville; 2003:195鈥?25. Malaga/Seville, 2002/2003
  2. Dhompongsa S, Fupinwong W, Kaewkhao A: Common fixed points of a nonexpansive semigroup and a convergence theorem for Mann iterations in geodesic metric spaces. / Nonlinear Anal. 2009, 70:4268鈥?273. CrossRef
  3. Leustean L: A quadratic rate of asymptotic regularity for -spaces. / J. Math. Anal. Appl. 2007, 325:386鈥?99. CrossRef
  4. Nanjaras B, Panyanak B: Demiclosedness principle for asymptotically nonexpansive mappings in spaces. / Fixed Point Theory Appl. 2010., 2010: Article ID 268780
  5. Niwongsa Y, Panyanak B: Noor iterations for asymptotically nonexpansive mappings in spaces. / Int. J. Math. Anal. 2010, 4:645鈥?56.
  6. Bridson M, Haefliger A: / Metric Spaces of Non-Positive Curvature. Springer, Berlin; 1999. CrossRef
  7. Bruhat F, Tits J: Groupes r茅ductifs sur un corps local I: Donn茅es radicielles valu茅es. / Publ. Math. Inst. Hautes 脡tudes Sci. 1972, 41:5鈥?51. CrossRef
  8. Dhompongsa S, Panyanak B: On 螖-convergence theorems in spaces. / Comput. Math. Appl. 2008, 56:2572鈥?579. CrossRef
  9. Khamsi MA, Kirk WA: / An Introduction to Metric Spaces and Fixed Point Theory. Wiley-Interscience, New York; 2001. CrossRef
  10. Ibn Dehaish BA: Ishikawa iteration process for asymptotic pointwise nonexpansive mappings in metric spaces. / Fixed Point Theory Appl. 2013., 2013: Article ID 98
  11. Ibn Dehaish BA, Khamsi MA, Khan AR: Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces. / J. Math. Anal. Appl. 2013, 397:861鈥?68. CrossRef
  12. Xu HK: Existence and convergence for fixed points of mappings of asymptotically nonexpansive type. / Nonlinear Anal. 1991, 16:1139鈥?146. CrossRef
  13. Chang SS, Chu YJ, Kim JK, Kim KH: Iterative approximation of fixed points for asymptotically nonexpansive type mappings in Banach spaces. / Panam. Math. J. 2001, 11:53鈥?3.
  14. Cho YJ, Zhou H, Hyun HG, Kim JK: Convergence theorems of iterative sequences for asymptotically nonexpansive type mappings in Banach spaces. / Commun. Appl. Nonlinear Anal. 2003, 10:85鈥?2.
  15. Fukhar-ud-din H, Khan SH: Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications. / J. Math. Anal. Appl. 2007, 328:821鈥?29. CrossRef
  16. Fukhar-ud-din H, Khan AR: Approximating common fixed points of asymptotically nonexpansive maps in uniformly convex Banach spaces. / Comput. Math. Appl. 2007, 53:1349鈥?360. CrossRef
  17. Huang JC: On common fixed points of asymptotically nonexpansive mappings in the intermediate sense. / Czechoslov. Math. J. 2004, 54:1055鈥?063. CrossRef
  18. Khan AR: On modified Noor iterations for asymptotically nonexpansive mappings. / Bull. Belg. Math. Soc. Simon Stevin 2010, 17:127鈥?40.
  19. Khan AR, Fukhar-ud-din H, Khan MAA: An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces. / Fixed Point Theory Appl. 2012., 2012: Article ID 54
  20. Khan SH, Fukhar-ud-din H: Weak and strong convergence of a scheme with errors for two nonexpansive mappings. / Nonlinear Anal. 2005, 61:1295鈥?301. CrossRef
  21. Khan SH, Takahashi W: Approximating common fixed points of two asymptotically nonexpansive mappings. / Sci. Math. Jpn. 2001, 53:143鈥?48.
  22. Kim GE, Kiuchi H, Takahashi W: Weak and strong convergence of Ishikawa iterations for asymptotically nonexpansive mappings in the intermediate sense. / Sci. Math. Jpn. 2004, 60:95鈥?06.
  23. Li G: Asymptotic behavior for commutative semigroups of asymptotically nonexpansive type mappings. / Nonlinear Anal. 2000, 42:175鈥?83. CrossRef
  24. Li G, Sims B: Fixed point theorems for mappings of asymptotically nonexpansive type. / Nonlinear Anal. 2002, 50:1085鈥?091. CrossRef
  25. Berinde V: On the convergence of the Ishikawa iteration in the class of quasi contractive operators. / Acta Math. Univ. Comen. 2004,73(1):119鈥?26.
  26. Berinde V: A convergence theorem for Mann iteration in the class of Zamfirescu operators. / An. Univ. Vest. Timi艧., Ser. Mat.-Inf. 2007,45(1):33鈥?1.
  27. Berinde V: / Iterative Approximation of Fixed Points. Springer, Berlin; 2007.
  28. Schu J: Weak and strong convergence to fixed points of asymptotically nonexpansive mappings. / Bull. Aust. Math. Soc. 1991, 43:153鈥?59. CrossRef
  29. Schu J: Iterative construction of fixed points of asymptotically nonexpansive mappings. / J. Math. Anal. Appl. 1991, 158:407鈥?13. CrossRef
  30. Tan KK, Xu HK: Fixed point iteration processes for asymptotically nonexpansive mappings. / Proc. Am. Math. Soc. 1994, 122:733鈥?39. CrossRef
  
• 作者单位：Hafiz Fukhar-ud-din (1) (2)
  
  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia
  2. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan
  
• ISSN：1687-1812

文摘

We study strong convergence of an Ishikawa-type algorithm of two asymptotically nonexpansive type maps to their common fixed point on a space. Our work provides an affirmative answer to the question of Tan and Xu (Proc. Am. Math. Soc. 122:733-739, 1994); in particular, strong convergence of an Ishikawa-type algorithm of two asymptotically nonexpansive maps without the rate of convergence condition is obtained on a nonlinear domain. MSC: Primary 47H09; 47H10; secondary 49M05