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CONVERGENCE THEOREMS OF IMPLICIT ITERATION PROCESS WITH ERRORS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE IN BANACH SPACES
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  • Journal title : East Asian mathematical journal
  • Volume 28, Issue 1,  2012, pp.63-71
  • Publisher : Youngnam Mathematical Society
  • DOI : 10.7858/eamj.2012.28.1.063
 Title & Authors
CONVERGENCE THEOREMS OF IMPLICIT ITERATION PROCESS WITH ERRORS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE IN BANACH SPACES
Saluja, G.S.;
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 Abstract
The aim of this article is to study an implicit iteration process with errors for a finite family of non-Lipschitzian asymptotically non expansive mappings in the intermediate sense in Banach spaces. Also we establish some strong convergence theorems and a weak convergence theorem for said scheme to converge to a common fixed point for non Lipschitzian asymptotically nonexpansive mappings in the intermediate sense. The results presented in this paper extend and improve the corresponding results of [1], [3]-[8], [10]-[11], [13]-[14], [16] and many others.
 Keywords
Asymptotically nonexpansive mapping in the intermediate sense;common fixed point;implicit iteration process with errors;Banach space;strong convergence;weak convergence;
 Language
English
 Cited by
 References
1.
H. H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 202 (1996), 150-159. crossref(new window)

2.
R. Bruck, T. Kuczumow and S. Reich, Convergence of iterates of asymptotically nonex-pansive mappings in Banach spaces with the uniform Opial property, Collo. Math. 65 (1993), no. 2, 169-179.

3.
S. S. Chang and Y. J. Cho, The implicit iterative processes for asymptotically nonex-pansive mappings, Nonlinear Anal. Appl. 1 (2003), 369-382.

4.
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)

5.
J. Gornicki, Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces, Comment. Math. Univ. Carolin. 301 (1989), 249-252.

6.
F. Gu, Strong and weak convergence of implicit iterative process with errors for asymptotically nonexpansive mappings, J. Appl. Anal. 12 (2006), no. 2, 267-282.

7.
B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967), 957-961. crossref(new window)

8.
P. L. Lions, Approximation de points fixes de contractions, C. R. Acad. Sci. Paris Ser. I Math. 284 (1977), 1357-1359.

9.
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597. crossref(new window)

10.
M. O. Osilike, Implicit iteration process for common fixed point of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004), 73-81. crossref(new window)

11.
S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980), 287-292. crossref(new window)

12.
J. Schu, Weak and strong convergence theorems to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991), 153-159. crossref(new window)

13.
Z. Sun, Strong convergence of an implicit iteration process for a nite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003), no. 1, 351-358. crossref(new window)

14.
K. K. Tan and H. K. Xu, The nonlinear ergodic theorem for asymptotically nonexpansive mappings in banach spaces, Proc. Amer. Math. Soc. 114 (1992), 399-404. crossref(new window)

15.
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)

16.
R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992), 486-491. crossref(new window)

17.
H. K. Xu and R. G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001), 767-773. crossref(new window)

18.
Y. Y. Zhou and S. S. Chang, Convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 23 (2002), 911-921. crossref(new window)