A Refinement of Schwarz–Pick Lemma for Higher Derivatives

In this paper, a Schwarz–Pick estimate of a holomorphic self map f of the unit disc D having the expansion f ( w ) = c 0 + c n ( w − z ) n + … in a neighborhood of some z in D is given. This result is a refinement of the Schwarz–Pick lemma,...

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Main Authors:	Ern Gun Kwon, Jinkee Lee, Gun Kwon, Mi Hui Kim
Format:	Article
Language:	English
Published:	MDPI AG 2019-01-01
Series:	Mathematics
Subjects:	Schwarz Lemma maximum principle Littlewood inequality
Online Access:	http://www.mdpi.com/2227-7390/7/1/77

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spelling	doaj-603a32a57f25443a9f5c18fd5d58c4d12020-11-24T21:52:49ZengMDPI AGMathematics2227-73902019-01-01717710.3390/math7010077math7010077A Refinement of Schwarz–Pick Lemma for Higher DerivativesErn Gun Kwon0Jinkee Lee1Gun Kwon2Mi Hui Kim3Department of Mathematics Education, Andong National University, Andong 36729, KoreaDepartment of Mathematics, Pusan National University, Busan 46241, KoreaDepartment of Mechanical Engineering, Graduate School, Yeungnam University, Gyeongsan 38541, KoreaDepartment of Mathematics, Graduate School, Andong National University, Andong 36729, KoreaIn this paper, a Schwarz–Pick estimate of a holomorphic self map f of the unit disc D having the expansion f ( w ) = c 0 + c n ( w − z ) n + … in a neighborhood of some z in D is given. This result is a refinement of the Schwarz–Pick lemma, which improves a previous result of Shinji Yamashita.http://www.mdpi.com/2227-7390/7/1/77Schwarz Lemmamaximum principleLittlewood inequality
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Ern Gun Kwon Jinkee Lee Gun Kwon Mi Hui Kim
spellingShingle	Ern Gun Kwon Jinkee Lee Gun Kwon Mi Hui Kim A Refinement of Schwarz–Pick Lemma for Higher Derivatives Mathematics Schwarz Lemma maximum principle Littlewood inequality
author_facet	Ern Gun Kwon Jinkee Lee Gun Kwon Mi Hui Kim
author_sort	Ern Gun Kwon
title	A Refinement of Schwarz–Pick Lemma for Higher Derivatives
title_short	A Refinement of Schwarz–Pick Lemma for Higher Derivatives
title_full	A Refinement of Schwarz–Pick Lemma for Higher Derivatives
title_fullStr	A Refinement of Schwarz–Pick Lemma for Higher Derivatives
title_full_unstemmed	A Refinement of Schwarz–Pick Lemma for Higher Derivatives
title_sort	refinement of schwarz–pick lemma for higher derivatives
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-01-01
description	In this paper, a Schwarz–Pick estimate of a holomorphic self map f of the unit disc D having the expansion f ( w ) = c 0 + c n ( w − z ) n + … in a neighborhood of some z in D is given. This result is a refinement of the Schwarz–Pick lemma, which improves a previous result of Shinji Yamashita.
topic	Schwarz Lemma maximum principle Littlewood inequality
url	http://www.mdpi.com/2227-7390/7/1/77
work_keys_str_mv	AT erngunkwon arefinementofschwarzpicklemmaforhigherderivatives AT jinkeelee arefinementofschwarzpicklemmaforhigherderivatives AT gunkwon arefinementofschwarzpicklemmaforhigherderivatives AT mihuikim arefinementofschwarzpicklemmaforhigherderivatives AT erngunkwon refinementofschwarzpicklemmaforhigherderivatives AT jinkeelee refinementofschwarzpicklemmaforhigherderivatives AT gunkwon refinementofschwarzpicklemmaforhigherderivatives AT mihuikim refinementofschwarzpicklemmaforhigherderivatives
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A Refinement of Schwarz–Pick Lemma for Higher Derivatives

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