WEAK AND STRONG CONVERGENCE OF MANN`S-TYPE ITERATIONS FOR A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS

Title & Authors
WEAK AND STRONG CONVERGENCE OF MANN`S-TYPE ITERATIONS FOR A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS
Song, Yisheng; Chen, Rudong;

Abstract
Let K be a nonempty closed convex subset of a Banach space E. Suppose $\small{\{T_{n}\}}$ (n
Keywords
uniformly asymptotically regular sequence;a countable family of nonexpansive mappings;weak and strong convergence;Mann`s type iteration;
Language
English
Cited by
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3.
Fixed point theorems and iterative approximations for monotone nonexpansive mappings in ordered Banach spaces, Fixed Point Theory and Applications, 2016, 2016, 1
4.
Some convergence theorems of the Mann iteration for monotone α-nonexpansive mappings, Applied Mathematics and Computation, 2016, 287-288, 74
References
1.
S. Atsushiba and W. Takahashi, Strong convergence of Mann's-type iterations for nonexpansive semigroups in general Banach spaces, Nonlinear Anal. 61 (2005), no. 6, 881-899

2.
F. E. Browder, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660-665

3.
R. E. Bruck, A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, Israel J. Math. 32 (1979), no. 2-3, 107-116

4.
R. E. Bruck, On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces, Israel J. Math. 38 (1981), no. 4, 304-314

5.
J. G. Falset, W. Kaczor, T. Kuczumow, and S. Reich, Weak convergence theorems for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 43 (2001), no. 3, Ser. A: Theory Methods, 377-401

6.
J. S. Jung, Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 302 (2005), no. 2, 509-520

7.
W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510

8.
J. G. O'Hara, P. Pillay, and H. K. Xu, Iterative approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces, Nonlinear Anal. 54 (2003), no. 8, 1417-1426

9.
S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 67 (1979), no. 2, 274-276

10.
S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980), no. 1, 287-292

11.
T. Shimizu and W. Takahashi, Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211 (1997), no. 1, 71-83

12.
Y. Song and R. Chen, Iterative approximation to common fixed points of nonexpansive mapping sequences in reflexive Banach spaces, Nonlinear Anal. 66 (2007), no. 3, 591-603

13.
Y. Song, R. Chen, and H. Zhou, Viscosity approximation methods for nonexpansive mapping sequences in Banach spaces, Nonlinear Anal. 66 (2007), no. 5, 1016-1024

14.
W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, 2000

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), no. 2, 301-308

16.
H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. 16 (1991), no. 12, 1127-1138