Communications in Mathematical Analysis

A Simple Estimate of the Bloch Constant

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

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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

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

First available in Project Euclid: 9 May 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


Izuki, Mitsuo; Koyama, Takeshi; Noi, Takahiro; Takeuchi, Tatsuki. A Simple Estimate of the Bloch Constant. Commun. Math. Anal. 21 (2018), no. 1, 35--41.

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