A necessary and sufficient condition for the strong convergence of Lipschitzian pseudocontractive mapping in Banach spaces |
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| Authors: | Yu-Chao Tang Ji-Gen Peng Liang-Gen Hu Li-Wei Liu |
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| Institution: | 1. Institute for Information and System Science, Faculty of Science, Xi’an Jiaotong University, Xi’an 710049, PR China;2. Department of Mathematics, Nanchang University, Nanchang 330031, PR China;3. Department of Mathematics, Ningbo University, Ningbo 315211, PR China |
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| Abstract: | The purpose of this paper is to establish some necessary and sufficient conditions for the strong convergence of the Ishikawa iterative sequence and the Mann iterative sequence to a fixed point of pseudocontractive mapping in Banach spaces. Our results, to some extent, improve and extend the well-known result of S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44(1) (1974) 147–150.] to Banach spaces. |
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