[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2014.54.1.103

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

Gu, Zhaohui (Cisco School of Informatics, Guangdong University of Foreign Studies)
Li, Yongjin (Department of Mathematics, Sun Yat-Sen University)

Publication Information

Kyungpook Mathematical Journal / v.54, no.1, 2014 , pp. 103-111 More about this Journal

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;

Citations & Related Records

Reference

1	Liu Qi Hou, A convergence theorem for Ishikawa iterates of continuous generalized nonexpansive maps, J. Math. Anal. Appl., 165(1992), 305-309. DOI
2	P-E. Mainge, Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 325(2007), 469-479. DOI ScienceOn
3	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.
4	Song Yisheng, Chen Rudong, Iterative approximation to common fixed points of nonexpansive mapping sequences in reflexive Banach spaces, Nonlinear Anal., 66(2007), 591-603. DOI ScienceOn
5	Xu, Hong Kun, Inequalities in Banach spaces with applications, Nonlinear Anal, 16(1991), 1127-1138. DOI ScienceOn
6	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.
7	Chen Jianren, Li Zhongkai, Banach operator pair and common fixed points for nonexpansive maps, Nonlinear Anal., 74(2011), 3086-3090. DOI ScienceOn
8	V. Berinde, On the convergence of the Ishikawa iteration in the class of quasi contractive operators, Acta Math. Univ. Comenian., 73(2004), 119-126.
9	S. C. Bose,Common fixed points of mappings in a uniformly convex Banach space, J. London Math. Soc., 18(1978), 151-156.
10	S. S. Chang, The fixed point theorem of mean non-expansive mapping in Banach space, (Chinese) Acta Sichuan Univsity, 2(1975), 67-78.
11	C. E. Chidume, Chika Moore, Fixed point iteration for pseudo-contractive maps, Proc. Amer. Math. Soc., 127(1999), 1163-1170. DOI ScienceOn
12	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.
13	R. Espinola, N. Hussain, Common fixed points for multimaps in metric spaces, Fixed Point Theory Appl, 2010(2010), Article ID 204981, 14 pages.
14	S. Ishikawa, Fixed points by a new iterations method, Proc. Amer. Math. Soc., 44(1974), 147-150. DOI ScienceOn