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

Toshiyuki Sugawa, Takao Terada

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)167-173
Number of pages7
JournalMonatshefte fur Mathematik
Volume156
Issue number2
DOIs
Publication statusPublished - 2009 Feb

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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