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Radius problems for univalent functions

Published:2020-06-01 Issue:1 Volume:26 Page:111-115
ISSN:1869-6082
Container-title:Journal of Applied Analysis
language:
Short-container-title:

Author:

Sokół Janusz¹,Trabka-Wiȩcław Katarzyna²

Affiliation:

1. Faculty of Mathematics and Natural Sciences, University of Rzeszów, ul. Prof. Pigonia 1, 35-310Rzeszów, Poland

2. Mechanical Engineering Faculty, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618Lublin, Poland

Abstract

AbstractThis paper considers the following problem: for what value r,

{r<1}

a function that is univalent in the unit disk

{|z|<1}

and convex in the disk

{|z|<r}

becomes starlike in

{|z|<1}

. The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics

Link

https://www.degruyter.com/document/doi/10.1515/jaa-2020-2008/pdf

Reference34 articles.

1. Sur les fonctions en moyenne (ψ)⁢p(\psi)p-valentes;Ann. Univ. Mariae Curie-Skłodowska Sect. A,1958

2. Zwei Bemerkungen zur konformen Abbildung;Jahresber. Dtsch. Math.-Ver.,1933

3. Close-to-convex Schlicht functions;Michigan Math. J.,1952

4. Über die konforme Abbildund von Sterngebieten;Översikt Finska Vetenskaps Soc. Förhandlingar,1921

5. Radius of starlikeness for analytic functions with fixed second coefficient;Kyungpook Math. J.,2017

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