Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces |
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| Authors: | Xiaolong Qin Yeol Je Cho Jung Im Kang Shin Min Kang |
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| Institution: | 1. Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea;2. Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea;3. National Institute for Mathematical Sciences, 385-16, 3F Tower Koreana, Doryong-dong, Yuseong-gu, Daejeon 305-340, Republic of Korea |
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| Abstract: | In an infinite-dimensional Hilbert space, the normal Mann’s iteration algorithm has only weak convergence, in general, even for nonexpansive mappings. In order to get a strong convergence result, we modify the normal Mann’s iterative process for an infinite family of nonexpansive mappings in the framework of Banach spaces. Our results improve and extend the recent results announced by many others. |
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| Keywords: | 47H09 47H10 |
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