摘要:

The functiongis a quasi-starlike function with parameterM> 1 if there is a starlike functionfor whichf(z)=z+2z2+…is a bounded function in the classSof normalized univalent functions, a numberMis called admissible forf/f/Mis bounded by 1. In Section 2 the reflection principle is used to reprove a theorem of Dziubiński which gives necessary and sufficient conditions for ann- slit starlike function to yield a quasi-starlike function which is starlike. The same technique is used to prove that there are bounded starlike functions which are not quasi-starlike for any admissible parameter. In Section 3 a fixed point result is used to show that there are functions convex of order α for any α < 1, which are not quasi-starlike for some admissible parameters.

ISSN:0278-1077    

DOI:10.1080/17476939708815028

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

The paper contains two different topics. The first topic deals with the coefficient problem. It is shown that for a certain type of rational functions (depending on a parameterq) the validity of Robertson's inequalities fornless than or equal tofq− 1 is sufficient to conclude Bieberbach/de Branges' inequalities for alln. In the second topic is studied the “stability of niceness” of Robertson's functional forn= 4.

ISSN:0278-1077    

DOI:10.1080/17476939708815029

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

For each ρ⩽3 we give a sharp lower bound for the translation length of a hyperbolic element in a Fuchsian group whose axis passes through an elliptic fixed point of order ρ. The results yield a surprising dichotomy between the cases ρ odd or even. We relate this result to a theorem of Beardon concerning the translation lengths of hyperbolic elements whose axes meet at a given angle.

ISSN:0278-1077    

DOI:10.1080/17476939708815030

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939708815007

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor