Previous |  Up |  Next

Article

Title: Convergence theorems for a finite family of nonexpansive and asymptotically nonexpansive mappings (English)
Author: Sitthikul, Kittipong
Author: Saejung, Satit
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 48
Issue: 1
Year: 2009
Pages: 139-152
Summary lang: English
.
Category: math
.
Summary: In this paper, weak and strong convergence of finite step iteration sequences to a common fixed point for a pair of a finite family of nonexpansive mappings and a finite family of asymptotically nonexpansive mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented. (English)
Keyword: Nonexpansive mapping
Keyword: asymptotically nonexpansive mapping
Keyword: common fixed point
Keyword: finite-step iterative sequence
MSC: 47H09
MSC: 47H10
MSC: 47J25
idZBL: Zbl 1192.47063
idMR: MR2641954
.
Date available: 2010-02-11T13:59:25Z
Last updated: 2012-05-04
Stable URL: http://hdl.handle.net/10338.dmlcz/137510
.
Reference: [1] Chidume, C. E., Ali, B.: Approximation of common fixed points for finite families of nonself asymptotically nonexpansive mappings in Banach spaces.J. Math. Anal. Appl. 326, 2 (2007), 960–973. Zbl 1112.47053, MR 2280956
Reference: [2] Chidume, C. E., Ali, B.: Weak and strong convergence theorems for finite families of asymptotically nonexpansive mappings in Banach spaces.J. Math. Anal. Appl. 330, 1 (2007), 377–387. Zbl 1141.47039, MR 2302930
Reference: [3] Cho, Y. J., Zhou, H., Guo, G.: Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings.Comput. Math. Appl. 47, 4-5 (2004), 707–717. Zbl 1081.47063, MR 2051342
Reference: [4] Clarkson, J. A.: Uniformly convex spaces.Trans. Amer. Math. Soc. 40, 3 (1936), 396–414. Zbl 0015.35604, MR 1501880
Reference: [5] García-Falset, J., Kaczor, W., Kuczumow, T., Reich, S.: Weak convergence theorems for asymptotically nonexpansive mappings and semigroups.Nonlinear Anal., Ser. A: Theory Methods 43, 3 (2001), 377–401. MR 1796983
Reference: [6] Goebel, K., Kirk, W. A.: A fixed point theorem for asymptotically nonexpansive mappings.Proc. Amer. Math. Soc. 35 (1972), 171–174. Zbl 0256.47045, MR 0298500
Reference: [7] Gornicki, J.: Weak and strong convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces.Comment. Math. Univ. Carolin 30 (1989), 249–252. MR 1014125
Reference: [8] Ishikawa, S.: Fixed points by new iteration method.Proc. Amer. Math. Soc. 44 (1974), 147–150. MR 0336469
Reference: [9] Liu, Z., Agarwal, R. P., Feng, C., Kang, S. M.: Weak and strong convergence theorems of common fixed points for a pair of nonexpansive and asymptotically nonexpansive mappings.Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 44 (2005), 83–96. Zbl 1099.47057, MR 2218570
Reference: [10] Liu, Z., Feng, C., Ume, J. S., Kang, S. M.: Weak and strong convergence for common fixed points of a pair of nonexpansive and asymptotically nonexpansive mappings.Taiwanese J. Math. 11, 1 (2007), 27–42. Zbl 1151.47060, MR 2304002
Reference: [11] Mann, W. R.: Mean value methods in iteration.Proc. Amer. Math. Soc. 4 (1953), 506–510. Zbl 0050.11603, MR 0054846
Reference: [12] Opial, Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings.Bull. Amer. Math. Soc. 73 (1967), 591–597. Zbl 0179.19902, MR 0211301
Reference: [13] Osilike, M. O., Aniagbosor, S. C.: Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings.Math. Comput. Modelling 32, 10 (2000), 1181–1191. Zbl 0971.47038, MR 1791754
Reference: [14] Schu, J.: Iterative construction of fixed points of asymptotically nonexpansive mappings.J. Math. Anal. Appl. 158, 2 (1991), 407–413. Zbl 0734.47036, MR 1117571
Reference: [15] Schu, J.: Weak and strong convergence to fixed points of asymptotically nonexpansive mappings.Bull. Austral. Math. Soc. 43, 1 (1991), 153–159. Zbl 0709.47051, MR 1086729
Reference: [16] Senter, H. F., Dotson, W. G., Jr: Approximating fixed points of nonexpansive mappings.Proc. Amer. Math. Soc. 44 (1974), 375–380. Zbl 0299.47032, MR 0346608
Reference: [17] Tan, K. K., Xu, H. K.: Fixed point iteration processes for asymptotically nonexpansive mappings.Proc. Amer. Math. Soc. 122 (1994), 733–739. Zbl 0820.47071, MR 1203993
Reference: [18] Thakur, B. S., Jung, J. S.: Weak and strong convergence of multistep iteration for finite family of asymptotically nonexpansive mappings.Fixed Point Theory Appl., Art. ID 31056 (2007), 15 pp. Zbl 1155.47315, MR 2335967
Reference: [19] Xu, B., Noor, M. A.: Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces.J. Math. Anal. Appl. 267 (2002), 444–453. Zbl 1011.47039, MR 1888015
Reference: [20] Zhou, Y. Y., Chang, S. S.: Convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in Banach spaces.Numer. Funct. Anal. and Optimiz. 23 (2002), 911–921. MR 1938840
.

Files

Files Size Format View
ActaOlom_48-2009-1_12.pdf 255.2Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo