STRONG CONVERGENCE THEOREMS FOR INFINITE COUNTABLE NONEXPANSIVE MAPPINGS AND IMAGE RECOVERY PROBLEM

Title & Authors
STRONG CONVERGENCE THEOREMS FOR INFINITE COUNTABLE NONEXPANSIVE MAPPINGS AND IMAGE RECOVERY PROBLEM
Yao, Yonghong; Liou, Yeong-Cheng;

Abstract
In this paper, we introduce an iterative scheme given by infinite nonexpansive mappings in Banach spaces. We prove strong convergence theorems which are connected with the problem of image recovery. Our results enrich and complement the recent many results.
Keywords
nonexpansive mapping;strong convergence;uniformly $\small{G{\hat{a}}teaux}$ differentiable norm;fixed point;
Language
English
Cited by
1.
A strong convergence of a modified Krasnoselskii‐Mann method for non‐expansive mappings in Hilbert spaces, Mathematical Modelling and Analysis, 2010, 15, 2, 265
References
1.
S. S. Chang, Some problems and results in the study of nonlinear analysis, Nonlinear Anal. 30 (1997), no. 7, 4197-4208

2.
S. S. Chang, Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 323 (2006), no. 2, 1402-1416

3.
G. Das and J. P. Debata, Fixed points of quasinonexpansive mappings, Indian J. Pure Appl. Math. 17 (1986), no. 11, 1263-1269

4.
S. Kitahara and W. Takahashi, Image recovery by convex combinations of sunny nonexpansive retractions, Topol. Methods Nonlinear Anal. 2 (1993), no. 2, 333-342

5.
P. Kuhfittig, Common fixed points of nonexpansive mappings by iteration, Pacific J. Math. 97 (1981), no. 1, 137-139

6.
C. H. Morales and J. S. Jung, Convergence of paths for pseudocontractive mappings in Banach spaces, Proc. Amer. Math. Soc. 128 (2000), no. 11, 3411-3419

7.
J. G. O'Hara, P. Pillay, and H. K. Xu, Iterative approaches to convex feasibility problems in Banach spaces, Nonlinear Anal. 64 (2006), no. 9, 2022-2042

8.
K. Shimoji and W. Takahashi, Strong convergence to common fixed points of infinite nonexpansive mappings and applications, Taiwanese J. Math. 5 (2001), no. 2, 387-404

9.
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

10.
Y. Song, Strong convergence theorems on an iterative method for a family of finite nonexpansive mappings, Appl. Math. Comput. 180 (2006), no. 1, 275-287

11.
T. Suzuki, Strong convergence of Krasnoselskii and Mann's type sequences for oneparameter nonexpansive semigroups without Bochner integrals, J. Math. Anal. Appl. 305 (2005), no. 1, 227-239

12.
W. Takahashi, Fixed point theorems and nonlinear ergodic theorems for nonlinear semigroups and their applications, Proceedings of the Second World Congress of Nonlinear Analysts, Part 2 (Athens, 1996). Nonlinear Anal. 30 (1997), no. 2, 1283-1293

13.
W. Takahashi, Nonlinear Functional Analysis, Kindai-kagakusha, Tokyo, 1988

14.
W. Takahashi and K. Shimoji, Convergence theorems for nonexpansive mappings and feasibility problems, Math. Comput. Modelling 32 (2000), no. 11-13, 1463-1471

15.
W. Takahashi and T. Tamura, Limit theorems of operators by convex combinations of nonexpansive retractions in Banach spaces, J. Approx. Theory 91 (1997), no. 3, 386-397

16.
H. K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl. 116 (2003), no. 3, 659-678

17.
H. Y. Zhou, L. Wei, and Y. J. Cho, Strong convergence theorems on an iterative method for a family of finite nonexpansive mappings in reflexive Banach spaces, Appl. Math. Comput. 173 (2006), no. 1, 196-212