Communications in Mathematical Analysis

A Simple Estimate of the Bloch Constant

Mitsuo Izuki, Takeshi Koyama, Takahiro Noi, and Tatsuki Takeuchi

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Abstract

Our aim is to give a simple estimate of the Bloch constant applying some fundamental facts on complex analysis. Our method is based on the Cauchy estimate, the maximum modulus principle, the Schwarz lemma and the Rouche theorem.

Article information

Source
Commun. Math. Anal., Volume 21, Number 1 (2018), 35-41.

Dates
First available in Project Euclid: 9 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.cma/1525831214

Mathematical Reviews number (MathSciNet)
MR3789416

Zentralblatt MATH identifier
1391.30042

Subjects
Primary: 30D20: Entire functions, general theory 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination

Keywords
Bloch theorem Bloch constant the Cauchy estimate the maximum modulus principle the Schwarz lemma the Rouché theorem

Citation

Izuki, Mitsuo; Koyama, Takeshi; Noi, Takahiro; Takeuchi, Tatsuki. A Simple Estimate of the Bloch Constant. Commun. Math. Anal. 21 (2018), no. 1, 35--41. https://projecteuclid.org/euclid.cma/1525831214


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