Halpern iteration in CAT(κ) spaces

Bozena Pia̧tek

doi:10.1007/s10114-011-9312-7

Halpern iteration in CAT(κ) spaces

Bozena Pia̧tek

Katedra Matematyki (RMS/RMS1)

Wyniki badań: Wkład do czasopisma › Artykuł › recenzja

29 Cytowania z bazy Scopus

Abstrakt

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.

Język oryginału	angielski
Strony (od–do)	635-646
Liczba stron	12
Czasopismo	Acta Mathematica Sinica, English Series
Tom	27
Numer wydania	4
Identyfikatory DOI	https://doi.org/10.1007/s10114-011-9312-7
Status publikacji	Opublikowano - kwi 2011

Obszary tematyczne ASJC Scopus

Matematyka ogólna
Matematyka stosowana

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10.1007/s10114-011-9312-7

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Cytowanie

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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., L{\'o}pez, G., Mart{\'i}n-M{\'a}rquez, 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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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.

KW - CAT(κ) spaces

KW - iterative methods

KW - metric trees

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SP - 635

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 4

ER -

Halpern iteration in CAT(κ) spaces

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