Directional convexity of level lines for functions convex in a given direction

Authors:
Dmitri V. Prokhorov and Jan Szynal

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1453-1457

MSC (2000):
Primary 30C20; Secondary 30C45

Published electronically:
September 19, 2002

MathSciNet review:
1949875

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the class of functions which are holomorphic and convex in direction in the unit disk , i.e. the domain is such that the intersection of and any straight line is a connected or empty set. In this note we determine the radius of the biggest disk with the property that each function maps this disk onto the convex domain in the direction .

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Additional Information

**Dmitri V. Prokhorov**

Affiliation:
Department of Mathematics, Saratov State University, 410026 Saratov, Russia

Email:
ProkhorovDV@info.sgu.ru

**Jan Szynal**

Affiliation:
Department of Mathematics, M. Curie-Skłodowska University, 20-031 Lublin, Poland

Email:
jsszynal@golem.umcs.lublin.pl

DOI:
http://dx.doi.org/10.1090/S0002-9939-02-06675-3

Keywords:
Level curves of holomorphic functions,
functions convex in one direction

Received by editor(s):
August 21, 2001

Received by editor(s) in revised form:
December 7, 2001

Published electronically:
September 19, 2002

Additional Notes:
The first author was partially supported by the RFBR Grant No. 01-01-00123 and the INTAS Grant No. 99-00089

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2002
American Mathematical Society