Halpern iteration in CAT(κ) spaces

Bozena Pia̧tek

doi:10.1007/s10114-011-9312-7

Halpern iteration in CAT(κ) spaces

Bozena Pia̧tek

Department of Mathematics (RMS/RMS1)

Research output: Contribution to journal › Article › peer-review

29 Citations (Scopus)

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.

Original language	English
Pages (from-to)	635-646
Number of pages	12
Journal	Acta Mathematica Sinica, English Series
Volume	27
Issue number	4
DOIs	https://doi.org/10.1007/s10114-011-9312-7
Publication status	Published - Apr 2011

Keywords

CAT(κ) spaces
iterative methods
metric trees

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s10114-011-9312-7

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AB - 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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KW - metric trees

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Halpern iteration in CAT(κ) spaces

Abstract

Keywords

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