A note on multivalence of functions of bounded index

Author:
Gerd H. Fricke

Journal:
Proc. Amer. Math. Soc. **40** (1973), 140-142

MSC:
Primary 30A66; Secondary 30A36

DOI:
https://doi.org/10.1090/S0002-9939-1973-0320315-9

MathSciNet review:
0320315

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper examines the relationship between the concept of bounded index and the radius of univalence, respectively -valence, of entire functions and their derivatives at arbitrary points in the plane.

**[1]**J. Clunie and F. R. Keogh,*On starlike and convex schlicht functions*, J. London Math. Soc.**35**(1960), 229–233. MR**0110814**, https://doi.org/10.1112/jlms/s1-35.2.229**[2]**Gerd H. Fricke,*A characterization of functions of bounded index*, Indian J. Math.**14**(1972), 207–212. MR**0355048****[3]**W. K. Hayman,*Multivalent functions*, Cambridge Tracts in Mathematics and Mathematical Physics, No. 48, Cambridge University Press, Cambridge, 1958. MR**0108586****[4]**Benjamin Lepson,*Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index*, Entire Functions and Related Parts of Analysis (Proc. Sympos. Pure Math., LaJolla, Calif., 1966) Amer. Math. Soc., Providence, R.I., 1968, pp. 298–307. MR**0237788**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0320315-9

Keywords:
Functions of bounded index,
univalent,
-valent,
exponential type

Article copyright:
© Copyright 1973
American Mathematical Society