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A reconsideration on convergence of three-step iterations for asymptotically nonexpansive mappings |
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| Authors: | Weerayuth Nilsrakoo Satit Saejung |
| Institution: | aDepartment of Mathematics, Statistics and Computer, Ubon Rajathanee University, Ubon Ratchathani 34190, Thailand bDepartment of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand |
| Abstract: | We illustrate that the control conditions of the main convergence theorems of Yao and Noor Convergence of three-step iterations for asymptotically nonexpansive mappings, Appl. Math. Comput. in press] are incorrect. We also provide new control conditions which are complementary to Nilsrakoo and Saejung’s results W. Nilsrakoo, S. Saejung, A new three-step fixed point iteration scheme for asymptotically nonexpansive mappings, Appl. Math. Comput. 181 (2006) 1026–1034]. |
| Keywords: | Asymptotically nonexpansive mapping Uniformly convex Banach space Three-step iteration Convergence theorem |
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