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Convergence theorems of a family of uniformly (L, (alfa))-Lipschitz asymptotically quasi-nonexpansive type mappings

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EN
Abstrakty
EN
In this paper, we study the convergence of the Ishikawa iterative sequence of rank-r to common fixed points of a finite family of asymptotically quasi-nonexpansive type mappings in uniformly convex Banach spaces. Our results extend and improve some known recent results given in the literature
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Strony
877--886
Opis fizyczny
Bibliogr. 13 poz.
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autor
  • Department of Mathematics & Information Technology Govt. Nagarjuna P.G. College of Science Raipur (C.G.), India, saluja_1963@rediffmail.com
Bibliografia
  • [1] M. K. Ghosh, L. Debnath, Convergence of Ishikawa iterates of quasi-nonexpansive mappings, J. Math. Anal. Appl. 207(1997), 96–103.
  • [2] K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174.
  • [3] S. Ishikawa, Fixed point by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), 147–150.
  • [4] Q. H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings with error member, J. Math. Anal. Appl. 259 (2001), 18–24.
  • [5] Q. H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings with error member of uniformly convex Banach spaces, J. Math. Anal. Appl. 266 (2002), 468–471.
  • [6] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506–510.
  • [7] W. V. Petryshyn, T. E. Williamson, Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings, J. Math. Anal. Appl. 43 (1973), 459–497.
  • [8] J. Quan, S. S. Chang, X. J. Long, Approximation common fixed point of asymptotically quasi-nonexpansive-type mappings by the finite steps iterative sequences, Fixed Point Theory and Applications Volume 2006, Article ID 70830, pages 1–8.
  • [9] D. R. Sahu, On generalized Ishikawa iteration process and nonexpansive mappings in Banach spaces, Demonstratio Math. 36 (3) (2003), 721–734.
  • [10] D. R. Sahu, S. C. Shrivastava, B. L. Malager, Approximation of common fixed points of a family of asymptotically quasi-nonexpansive mappings, Demonstratio Math. 41 (3) (2008), 625–632.
  • [11] J. Schu, Weak and strong convergence theorems to fixed points of asymptotically non-expansive mappings, Bull. Austral. Math. Soc. 43 (1991), 153–159.
  • [12] K. K. Tan, H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), 301–308.
  • [13] K. K. Tan, H. K. Xu, Fixed point iteration processes for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 122 (1994), 733–739.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0031-0013
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