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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Weakly starlike meromorphic univalent functions


Authors: Richard J. Libera and Albert E. Livingston
Journal: Trans. Amer. Math. Soc. 202 (1975), 181-191
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9947-1975-0361036-2
MathSciNet review: 0361036
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Abstract: A weakly starlike meromorphic univalent function is one of the form $ f(z) = - \rho zg(z){[(z - \rho )(1 - \rho z)]^{ - 1}}$ for $ 0 < \rho < 1$ and $ g(z)$ a meromorphic starlike function. The behavior of coefficients and growth of this class of functions and of a subset are studied.


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  • [1] J. Clunie, On meromorphic schlicht functions, J. London Math. Soc. 34 (1959), 215-216. MR 21 #5737. MR 0107009 (21:5737)
  • [2] G. M. Goluzin, Geometric theory of functions of a complex variable, GITTL, Moscow, 1952; English transl., Transl. Math. Monographs, vol. 26, Amer. Math. Soc., Providence, R. I., 1969. MR 15, 112; 40 #308. MR 0247039 (40:308)
  • [3] J. Hummel, Extremal properties of weakly starlike $ p$-valent functions, Trans. Amer. Math. Soc. 130 (1968), 544-551. MR 36 #5332. MR 0222280 (36:5332)
  • [4] -, The coefficients of starlike functions, Proc. Amer. Math. Soc. 22 (1969), 311-315. MR 40 #4440. MR 0251209 (40:4440)
  • [5] K. Ladegast, Beiträge zur Theorie der schlichten Funktionen, Math. Z. 58 (1953), 115-159. MR 15, 24. MR 0056090 (15:24a)
  • [6] P. Montel, Leçons sur les fonctions univalentes ou multivalentes, Gauthier-Villars, Paris, 1933.
  • [7] C. Pommerenke, On starlike and convex functions, J. London Math. Soc. 37 (1962), 209-224. MR 25 #1279. MR 0137830 (25:1279)
  • [8] D. Styer, Multivalent meromorphic weakly starlike functions, Dissertation, University of Maryland, College Park, Md., 1970.

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DOI: https://doi.org/10.1090/S0002-9947-1975-0361036-2
Article copyright: © Copyright 1975 American Mathematical Society

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