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Mathematics 2019, 7(1), 77; https://doi.org/10.3390/math7010077

A Refinement of Schwarz–Pick Lemma for Higher Derivatives

1
Department of Mathematics Education, Andong National University, Andong 36729, Korea
2
Department of Mathematics, Pusan National University, Busan 46241, Korea
3
Department of Mechanical Engineering, Graduate School, Yeungnam University, Gyeongsan 38541, Korea
4
Department of Mathematics, Graduate School, Andong National University, Andong 36729, Korea
*
Author to whom correspondence should be addressed.
Received: 23 November 2018 / Revised: 26 December 2018 / Accepted: 10 January 2019 / Published: 13 January 2019
(This article belongs to the Section Mathematics and Computers Science)
Full-Text   |   PDF [207 KB, uploaded 13 January 2019]

Abstract

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. View Full-Text
Keywords: Schwarz Lemma; maximum principle; Littlewood inequality Schwarz Lemma; maximum principle; Littlewood inequality
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kwon, E.G.; Lee, J.; Kwon, G.; Kim, M.H. A Refinement of Schwarz–Pick Lemma for Higher Derivatives. Mathematics 2019, 7, 77.

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