Advanced SearchSearch Tips
Approximation of Common Fixed Points for a Family of Non-Lipschitzian Mappings
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 49, Issue 4,  2009, pp.701-712
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2009.49.4.701
 Title & Authors
Approximation of Common Fixed Points for a Family of Non-Lipschitzian Mappings
Kim, Tae-Hwa; Park, Yong-Kil;
  PDF(new window)
In this paper, we first introduce a family S = { : C C} of non-Lipschitzian mappings, called total asymptotically nonexpansive (briefly, TAN) on a nonempty closed convex subset C of a real Banach space X, and next give necessary and sufficient conditions for strong convergence of the sequence {} defined recursively by the algorithm = , , starting from an initial guess , to a common fixed point for such a continuous TAN family S in Banach spaces. Finally, some applications to a finite family of TAN self mappings are also added.
Common fixed points;non-Lipschitzian mappings;total asymptotically nonexpansive mappings;strong convergence;
 Cited by
Ya. I. Alber, C. E. Chidume and H. Zegeye, Approximating fixed points of total asymptotically nonexpansive mappings, Fixed Point Theory and Appl., 2006(2006), article ID 10673, 20 pages.

R. E. Bruck, T. Kuczumow and S. Reich, Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloq. Math., 65(1993), 169-179.

C. E. Chidume and E. U. Ofoedu, Approximation of common fixed points for finite families of total asymptotically nonexpansive mappings, J. Math. Anal. Appl., 333(2007), 128-141. crossref(new window)

K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35(1972), 171-174. crossref(new window)

K. Goebel and W.A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Univ. Press, Cambridge, 1990.

G. E. Kim and T. H. Kim, Mann and Ishikawa iterations with errors for non-Lipschitzian mappings in Banach spaces, Comput. Math. Appl., 42(2001), 1565-1570. crossref(new window)

W. A. Kirk, Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math., 17(1974), 339-346. crossref(new window)

M. O. Osilike, S. C. Aniagbosor, and B. G. Akuchu, Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces, PanAm. Math. J., 12(2002), 77-88.

W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, 2000.

K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178(1993), 301-308. crossref(new window)