Strong convergence theorems for multi-step Noor iterations with errors in Banach spaces |
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Authors: | Somyot Plubtieng |
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Institution: | Department of Mathematics, Faculty of Science, Naresuan University, Pitsanulok 65000, Thailand |
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Abstract: | In this paper, we established two strong convergence theorems for a multi-step Noor iterative scheme with errors for mappings of asymptotically nonexpansive in the intermediate sense(asymptotically quasi-nonexpansive, respectively) in Banach spaces. Our results extend and improve the recent ones announced by Xu and Noor B.L. Xu, M.A. Noor, Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444-453], Cho, Zhou and Guo Y.J. Cho, H. Zhou, G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47 (2004) 707-717], and many others. |
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Keywords: | Asymptotically nonexpansive in the intermediate sense Asymptotically quasi-nonexpansive mappings Completely continuous Uniformly convex Uniformly L-Lipschitzian |
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