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Radius problems associated with pre-Schwarzian and Schwarzian derivatives
-
Saminathan Ponnusamy
and
Toshiyuki Sugawa
Published/Copyright:
May 28, 2014
Abstract
Some of important univalence criteria for a non-constant meromorphic function f(z) on the unit disk π» involve its pre-Schwarzian or Schwarzian derivative. We consider an appropriate norm for the pre-Schwarzian derivative, and discuss the problem of finding the largest possible rβββ(0,β1) for which the pre-Schwarzian norm of the dilation rβ1f(rz) is not greater than a prescribed number for normalized univalent functions f(z) in the unit disk. Similar results concerning the Schwarzian derivative are also obtained.
Keywords: Univalent functions; radius property; pre-Schwarzian and Schwarzian derivatives; pre-Schwarzian and Schwarzian norms
AMS (2010): Primary 30C45; Secondary 30C55; 33C05
Received: 2013-7-10
Accepted: 2014-3-6
Published Online: 2014-5-28
Published in Print: 2014-6-28
Β©2014 Walter de Gruyter Berlin/Boston
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Keywords for this article
Univalent functions;
radius property;
pre-Schwarzian and Schwarzian derivatives;
pre-Schwarzian and Schwarzian norms
Articles in the same Issue
- Frontmatter
- Pseudo-orthants as a generalisation of orthants
- Uniqueness of meromorphic functions sharing three sets β Further study
- Radius problems associated with pre-Schwarzian and Schwarzian derivatives
- Entire functions sharing certain values with their derivatives
- Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers
- Local separability property for Reifenberg sets in parabolic space
- Sharp inequalities for the psi function and harmonic numbers
- Evolution of open elastic curves in βn subject to fixed length and natural boundary conditions
- Refinements of the Ostrowski inequality in terms of the cumulative variation and applications
- Erratum to Analysis 34(1), pg. 81β109
- 10.1515/anly-2014-0002
