A generalization of Suzuki's lemma

Let {zn}, {wn}, and {vn} be bounded sequences in a metric space of hyperbolic type (X, d), and let {αn} be a sequence in [0,1] with 0 < lim infnαn< lim supnαn< 1. If zn+1=αnwn(1-αn)vnfor all n ∈ ℕ , limnd (zn, vn) = 0, and lim supn(d (wn+1, wn) - d (zn+1, zn)) ≤ 0, then limnd (wn, zn) = 0....

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Main Authors:	B. Panyanak, A. Cuntavepanit
Format:	Journal
Published:	2018
Subjects:	Mathematics
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=80052686272&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50116
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Institution:	Chiang Mai University

id	th-cmuir.6653943832-50116
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spelling	th-cmuir.6653943832-501162018-09-04T04:24:32Z A generalization of Suzuki's lemma B. Panyanak A. Cuntavepanit Mathematics Let {zn}, {wn}, and {vn} be bounded sequences in a metric space of hyperbolic type (X, d), and let {αn} be a sequence in [0,1] with 0 < lim infnαn< lim supnαn< 1. If zn+1=αnwn(1-αn)vnfor all n ∈ ℕ , limnd (zn, vn) = 0, and lim supn(d (wn+1, wn) - d (zn+1, zn)) ≤ 0, then limnd (wn, zn) = 0. This is a generalization of Lemma 2.2 in (T. Suzuki, 2005). As a consequence, we obtain strong convergence theorems for the modified Halpern iterations of nonexpansive mappings in CAT(0) spaces. Copyright © 2011 B. Panyanak and A. Cuntavepanit. 2018-09-04T04:24:32Z 2018-09-04T04:24:32Z 2011-09-16 Journal 16870409 10853375 2-s2.0-80052686272 10.1155/2011/824718 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=80052686272&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50116
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Mathematics
spellingShingle	Mathematics B. Panyanak A. Cuntavepanit A generalization of Suzuki's lemma
description	Let {zn}, {wn}, and {vn} be bounded sequences in a metric space of hyperbolic type (X, d), and let {αn} be a sequence in [0,1] with 0 < lim infnαn< lim supnαn< 1. If zn+1=αnwn(1-αn)vnfor all n ∈ ℕ , limnd (zn, vn) = 0, and lim supn(d (wn+1, wn) - d (zn+1, zn)) ≤ 0, then limnd (wn, zn) = 0. This is a generalization of Lemma 2.2 in (T. Suzuki, 2005). As a consequence, we obtain strong convergence theorems for the modified Halpern iterations of nonexpansive mappings in CAT(0) spaces. Copyright © 2011 B. Panyanak and A. Cuntavepanit.
format	Journal
author	B. Panyanak A. Cuntavepanit
author_facet	B. Panyanak A. Cuntavepanit
author_sort	B. Panyanak
title	A generalization of Suzuki's lemma
title_short	A generalization of Suzuki's lemma
title_full	A generalization of Suzuki's lemma
title_fullStr	A generalization of Suzuki's lemma
title_full_unstemmed	A generalization of Suzuki's lemma
title_sort	generalization of suzuki's lemma
publishDate	2018
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=80052686272&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50116
_version_	1681423531944968192

A generalization of Suzuki's lemma

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