JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Approximation of Common Fixed Points of Mean Non-expansive Mapping in Banach Spaces
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 54, Issue 1,  2014, pp.103-111
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2014.54.1.103
 Title & Authors
Approximation of Common Fixed Points of Mean Non-expansive Mapping in Banach Spaces
Gu, Zhaohui; Li, Yongjin;
  PDF(new window)
 Abstract
Let X be a uniformly convex Banach space, and S, T be pair of mean nonexpansive mappings. Some necessary and sufficient conditions are given for Ishikawa iterative sequence converge to common fixed points, and we prove that the sequence of Ishikawa iterations associated with S and T converges to the common fixed point of S and T. This generalizes former results proved by Z. Gu and Y. Li [4].
 Keywords
Pair of mean non-expansive mappings;Ishikawa iteration;Common fixed point;
 Language
English
 Cited by
 References
1.
V. Berinde, On the convergence of the Ishikawa iteration in the class of quasi contractive operators, Acta Math. Univ. Comenian., 73(2004), 119-126.

2.
S. C. Bose,Common fixed points of mappings in a uniformly convex Banach space, J. London Math. Soc., 18(1978), 151-156.

3.
S. S. Chang, The fixed point theorem of mean non-expansive mapping in Banach space, (Chinese) Acta Sichuan Univsity, 2(1975), 67-78.

4.
Chen Jianren, Li Zhongkai, Banach operator pair and common fixed points for nonexpansive maps, Nonlinear Anal., 74(2011), 3086-3090. crossref(new window)

5.
C. E. Chidume, Chika Moore, Fixed point iteration for pseudo-contractive maps, Proc. Amer. Math. Soc., 127(1999), 1163-1170. crossref(new window)

6.
Lj. B. Ciric, J. S. Ume and M. S. Khan, On the convergence of the Ishikawa iterates to a common fixed point of two mappings, Arch. Math., 39(2003), 123-127.

7.
R. Espinola, N. Hussain, Common fixed points for multimaps in metric spaces, Fixed Point Theory Appl, 2010(2010), Article ID 204981, 14 pages.

8.
S. Ishikawa, Fixed points by a new iterations method, Proc. Amer. Math. Soc., 44(1974), 147-150. crossref(new window)

9.
Liu Qi Hou, A convergence theorem for Ishikawa iterates of continuous generalized nonexpansive maps, J. Math. Anal. Appl., 165(1992), 305-309. crossref(new window)

10.
P-E. Mainge, Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 325(2007), 469-479. crossref(new window)

11.
R. A. Rashwan, On the convergence of Mann iterates to a common fixed point for a pair of mappings, Demonstratio. Math., 33(1990), 709-712.

12.
Song Yisheng, Chen Rudong, Iterative approximation to common fixed points of nonexpansive mapping sequences in reflexive Banach spaces, Nonlinear Anal., 66(2007), 591-603. crossref(new window)

13.
Xu, Hong Kun, Inequalities in Banach spaces with applications, Nonlinear Anal, 16(1991), 1127-1138. crossref(new window)

14.
Zhaohui Gu, Yongjin Li, Approximation methods for common fixed points of mean nonexpansive mapping in Banach spaces, Fixed Point Theory and Applications, 2008 (2008), Article ID 471532, 7 pages.