Univalence criteria and analogues of the John constant

Authors

  • Y. C. Kim Yeungnam University
  • T. Sugawa Tohoku University

Keywords:

univalent function, univalence criterion, Grunsky coefficients

Abstract

Let $p(z)=zf'(z)/f(z)$ for a function $f(z)$ analytic on the unit disk $|z|<1$ in the complex plane and normalized by $f(0)=0, f'(0)=1.$ We will provide lower and upper bounds for the best constants $\delta_0$ and $\delta_1$ such that the conditions $|\log|p(z)||\le\delta_0/2$ and $\log|p(w)|-\log|p(z)|\le\delta_1$ for $|z|,|w|<1$ respectively imply univalence of $f$ on the unit disk. 10.1017/S0004972712000962

Published

2013-09-27

Issue

Vol. 88 No. 3 (2013)

Section

Articles
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