Browse > Article
http://dx.doi.org/10.4134/BKMS.2007.44.3.493

WEAK AND STRONG CONVERGENCE CRITERIA OF MODIFIED NOOR ITERATIONS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE  

Banerjee, Shrabani (DEPARTMENT OF MATHEMATICS BENGAL ENGINEERING AND SCIENCE UNIVERSITY)
Choudhury, Binayak Samadder (DEPARTMENT OF MATHEMATICS BENGAL ENGINEERING AND SCIENCE UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.44, no.3, 2007 , pp. 493-506 More about this Journal
Abstract
In this paper weak and strong convergence theorems of modified Noor iterations to fixed points for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces are established. In one theorem where we establish strong convergence we assume an additional property of the operator whereas in another theorem where we establish weak convergence assume an additional property of the space.
Keywords
asymptotically nonexpansive mapping in the intermediate sense; condition (A); uniformly convex; modified Noor iteration;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 Y. J. Cho, H. Y. Zhou, and G. Guo, Weak and strong convergence theorems for three- step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47 (2004), no. 4-5, 707-717   DOI   ScienceOn
2 T. Hicks and J. Kubicek, On the Mann iteration process in a Hilbert space, J. Math. Anal. Appl. 59 (1977), no. 3, 498-504   DOI
3 M. Aslam Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251 (2000), no. 1, 217-229   DOI   ScienceOn
4 J. Schu, Iterative construction of ?xed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991), no. 2, 407-413   DOI
5 W. A. Kirk, Fixed point theorems for non-Lipschitzian mappings of asymptotically non-expansive type, Israel J. Math. 17 (1974), 339-346   DOI
6 S. Ishikawa, Fixed points by a new iteration, Proc. Amer. Math. Soc. 44 (1974), 147-150
7 R. Bruck, T. Kuczumow, and S. Reich, Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloq. Math. 65 (1993), no. 2, 169-179   DOI
8 R. Glowinski and P. Le Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM Studies in Applied Mathematics, 9. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1989
9 K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171-174
10 S. Haubruge, V. H. Nguyen, and J. J. Strodiot, Convergence analysis and applications of the Glowinski-Le Tallec splitting method for finding a zero of the sum of two maximal monotone operators, J. Optim. Theory Appl. 97 (1998), no. 3, 645-673   DOI   ScienceOn
11 G. E. Kim and T. H. Kim, Mann and Ishikawa iterations with errors for non- Lipschitzian mappings in Banach spaces, Comput. Math. Appl. 42 (2001), no. 12, 1565- 1570   DOI   ScienceOn
12 W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506- 510
13 K. Nammanee, M. A. Noor, and S. Suantai, Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 314 (2006), no. 1, 320-334   DOI   ScienceOn
14 K. Nammanee and S. Suantai, The modified Noor iterations with errors for non- Lipschitzian mappings in Banach spaces, Applied Mathematics and Computation 187 (2007), 669-679   DOI   ScienceOn
15 M. Aslam Noor, Three-step iterative algorithms for multivalued quasi variational inclusions, J. Math. Anal. Appl. 255 (2001), no. 2, 589-604   DOI   ScienceOn
16 Z. Opial, Weak convergence of the sequence of successive approximation for nonexpan- sive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597   DOI
17 S. Plubtieng and R. Wangkeeree, Strong convergence theorems for multi-step Noor it-erations with errors in Banach spaces, J. Math. Anal. Appl. 321 (2006), no. 1, 10-23   DOI   ScienceOn
18 H. F. Senter and W. G. Jr. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974), 375-380
19 B. E. Rhoades, Fixed point iterations for certain nonlinear mappings, J. Math. Anal. Appl. 183 (1994), no. 1, 118-120   DOI   ScienceOn
20 J. Schu, Weak and strong convergence to ?xed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991), no. 1, 153-159   DOI
21 S. Suantai, Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 311 (2005), no. 2, 506-517   DOI   ScienceOn
22 K. K. Tan and H. K. Hu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), no. 2, 301-308   DOI   ScienceOn
23 H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. 16 (1991), no. 12, 1127-1138   DOI   ScienceOn
24 H. K. Xu, Existence and convergence for ?xed points of mappings of asymptotically non- expansive type, Nonlinear Anal. 16 (1991), no. 12, 1139-1146   DOI   ScienceOn
25 B. L. Xu and M. A. Noor, Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002), no. 2, 444-453   DOI   ScienceOn