On the univalence of some classes of regular functions

Authors:
R. J. Libera and A. E. Livingston

Journal:
Proc. Amer. Math. Soc. **30** (1971), 327-336

MSC:
Primary 30.42

MathSciNet review:
0288244

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Abstract: Let be regular in the unit disk and normalized by the conditions and and let . The paper deals with the mapping properties of when is known. For example, if is starlike of order , then the disk in which is always starlike of order , is determined. All results are sharp.

**[1]**Richard J. Libera,*Some radius of convexity problems*, Duke Math. J.**31**(1964), 143–158. MR**0160890****[2]**R. J. Libera,*Some classes of regular univalent functions*, Proc. Amer. Math. Soc.**16**(1965), 755–758. MR**0178131**, 10.1090/S0002-9939-1965-0178131-2**[3]**A. E. Livingston,*On the radius of univalence of certain analytic functions*, Proc. Amer. Math. Soc.**17**(1966), 352–357. MR**0188423**, 10.1090/S0002-9939-1966-0188423-X**[4]**Zeev Nehari,*Conformal mapping*, McGraw-Hill Book Co., Inc., New York, Toronto, London, 1952. MR**0045823****[5]**K. S. Padmanabhan,*On the radius of univalence of certain classes of analytic functions.*, J. London Math. Soc. (2)**1**(1969), 225–231. MR**0247062****[6]**Pasquale Porcelli,*Linear spaces of analytic functions*, Rand McNally & Co., Chicago, Ill., 1966. MR**0259581**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1971-0288244-5

Keywords:
Univalent function,
starlike function of order ,
radius of starlikeness of order ,
function with positive real part

Article copyright:
© Copyright 1971
American Mathematical Society