A coefficient inequality for Bloch functions with applications to uniformly locally univalent functions

Toshiyuki Sugawa; Takao Terada

doi:10.1007/s00605-008-0548-y

A coefficient inequality for Bloch functions with applications to uniformly locally univalent functions

Toshiyuki Sugawa, Takao Terada

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

3 Citations (Scopus)

Abstract

We give a Fekete-Szegö type inequality for an analytic function on the unit disk with Bloch seminorm ≤ 1. As an application of it, we derive a sharp inequality for the third coefficient of a uniformly locally univalent function f(z) = z + a ₂ z ² + a ₃ z ³ + ⋯ on the unit disk with pre-Schwarzian norm ≤ λ for a given λ > 0.

Original language	English
Pages (from-to)	167-173
Number of pages	7
Journal	Monatshefte fur Mathematik
Volume	156
Issue number	2
DOIs	https://doi.org/10.1007/s00605-008-0548-y
Publication status	Published - 2009 Feb
Externally published	Yes

Keywords

Bloch function
Error function
Fekete-Szegö inequality
Pre-Schwarzian derivative
Uniformly locally univalent function

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00605-008-0548-y

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title = "A coefficient inequality for Bloch functions with applications to uniformly locally univalent functions",

abstract = "We give a Fekete-Szeg{\"o} type inequality for an analytic function on the unit disk with Bloch seminorm ≤ 1. As an application of it, we derive a sharp inequality for the third coefficient of a uniformly locally univalent function f(z) = z + a 2 z 2 + a 3 z 3 + ⋯ on the unit disk with pre-Schwarzian norm ≤ λ for a given λ > 0.",

keywords = "Bloch function, Error function, Fekete-Szeg{\"o} inequality, Pre-Schwarzian derivative, Uniformly locally univalent function",

author = "Toshiyuki Sugawa and Takao Terada",

note = "Funding Information: The first author was partially supported by the JSPS Grant-in-Aid for Scientific Research (B), 17340039. ",

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T1 - A coefficient inequality for Bloch functions with applications to uniformly locally univalent functions

AU - Sugawa, Toshiyuki

AU - Terada, Takao

N1 - Funding Information: The first author was partially supported by the JSPS Grant-in-Aid for Scientific Research (B), 17340039.

PY - 2009/2

Y1 - 2009/2

N2 - We give a Fekete-Szegö type inequality for an analytic function on the unit disk with Bloch seminorm ≤ 1. As an application of it, we derive a sharp inequality for the third coefficient of a uniformly locally univalent function f(z) = z + a 2 z 2 + a 3 z 3 + ⋯ on the unit disk with pre-Schwarzian norm ≤ λ for a given λ > 0.

AB - We give a Fekete-Szegö type inequality for an analytic function on the unit disk with Bloch seminorm ≤ 1. As an application of it, we derive a sharp inequality for the third coefficient of a uniformly locally univalent function f(z) = z + a 2 z 2 + a 3 z 3 + ⋯ on the unit disk with pre-Schwarzian norm ≤ λ for a given λ > 0.

KW - Bloch function

KW - Error function

KW - Fekete-Szegö inequality

KW - Pre-Schwarzian derivative

KW - Uniformly locally univalent function

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JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 2

ER -

A coefficient inequality for Bloch functions with applications to uniformly locally univalent functions

Abstract

Keywords

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