Convergence criteria of modified Noor iterations with errors for three asymptotically nonexpansive nonself-mappings

Thianwan, Tanakit ¹

¹ Department of Mathematics, Faculty of Science, University of Phayao, Phayao, 56000, Thailand

Journal of nonlinear sciences and its applications, Tome 6 (2013) no. 3, p. 181-197.

Résumé

The aim of this paper, is to introduce and study the modified Noor iterative algorithm with errors for approximating common fixed points of three asymptotically nonexpansive nonself-mappings. Several strong and weak convergence results on this algorithm are established under certain conditions in a uniformly convex Banach space. The results obtained in this paper improve and generalize the recent ones announced by Khan and Hussain [S. H. Khan, N. Hussain, Comput. Math. Appl. 55 (2008), 2544-2553.], Nammanee, et. al., [K. Nammanee, M.A. Noor and S. Suantai, J. Math. Anal. Appl. 314 (2006), 320-334.], Suantai [S. Suantai, J. Math. Anal. Appl. 311 (2005), 506-517.], Cho et. al., [Y. J. Cho, H. Y. Zhou and G. Guo, Comput. Math. Appl. 47 (2004), 707-717.], Xu and Noor [B. L. Xu and M.A. Noor, J. Math. Anal. Appl. 267 (2002), 444-453.] and many others.

Détail

DOI : 10.22436/jnsa.006.03.04

Classification : 47H10, 47H09, 46B20
Keywords: Asymptotically nonexpansive nonself-mapping, weak and strong convergence, completely continuous, Opial's condition, common fixed points.

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