| Halpern Iteration in CAT（k） Spaces |
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| 作者姓名： | Bozena PIATEK |
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| 作者单位： | Silesian University of Technology, Institute of Mathematics, 44-100 Gliwice, Poland |
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| 摘 要： |
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| 关 键 词： | 迭代算法 Hadamard流形 空间 CAT 非扩张映象 序列收敛 迭代程序 集值映射 |
Halpern iteration in CAT(<Emphasis Type="Italic">κ</Emphasis>) spaces |
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| Bozena PIATEK.Halpern iteration in CAT(κ) spaces[J].Acta Mathematica Sinica,2011,27(4):635-646. |
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| Authors: | Bożena Piątek |
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| Institution: | 1.Institute of Mathematics,Silesian University of Technology,Gliwice,Poland |
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| Abstract: | In this paper we show that an iterative sequence generated by the Halpern algorithm converges to a fixed point in the case
of complete CAT(κ) spaces. Similar results for Hadamard manifolds were obtained in Li, C., López, G., Martín-Márquez, V.: Iterative algorithms
for nonexpansive mappings on Hadamard manifolds. Taiwanese J. Math., 14, 541–559 (2010)], but we study a much more general case. Moreover, we discuss the Halpern iteration procedure for set-valued
mappings. |
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| Keywords: | CAT（k） spaces metric trees iterative methods |
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