Approximation of Common Fixed Points of Mean Non-expansive Mapping in Banach Spaces

- 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;

Gu, Zhaohui; Li, Yongjin;

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

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.

5.

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

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.

9.

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

10.

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

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.

13.

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.