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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Piątek, B. Halpern iteration in CAT(κ) spaces. Acta. Math. Sin.-English Ser. 27, 635–646 (2011). https://doi.org/10.1007/s10114-011-9312-7
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DOI: https://doi.org/10.1007/s10114-011-9312-7