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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Starlike meromorphic functions


Author: James Miller
Journal: Proc. Amer. Math. Soc. 31 (1972), 446-452
DOI: https://doi.org/10.1090/S0002-9939-1972-0288267-7
MathSciNet review: 0288267
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Abstract | References | Additional Information

Abstract: In this paper we study meromorphic univalent functions which map the unit disk onto the exterior of a domain which is starlike with respect to some finite point different from the origin. We obtain bounds on the arc length, an integral representation, and bounds on the maximum modulus of starlike meromorphic functions.


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  • [1] W. Hayman, On functions with positive real part, J. London Math. Soc. 36 (1961), 35-48. MR 27 #311. MR 0150310 (27:311)
  • [2] J. A. Jenkins, On a conjecture of Goodman concerning meromorphic univalent functions, Michigan Math. J. 9 (1962), 25-27. MR 24 #A2017. MR 0132170 (24:A2017)
  • [3] F. R. Keogh, Some theorems on conformal mapping of bounded starshaped domains, Proc. London Math. Soc. (3) 9 (1959), 481-491. MR 22 #1683. MR 0110815 (22:1683)
  • [4] Y. Komatu, Note on the theory of conformal representation by meromorphic functions. I, II, Proc. Japan Acad. 21 (1945), 269-284. MR 11, 170. MR 0031564 (11:170a)
  • [5] J. Miller, Convex meromorphic mappings and related functions, Proc. Amer. Math. Soc. 25 (1970), 220-228. MR 41 #3740. MR 0259098 (41:3740)
  • [6] Ch. Pommerenke, On starlike and convex functions, J. London Math. Soc. 37 (1962), 209-224. MR 25 #1279. MR 0137830 (25:1279)
  • [7] M. Robertson, Star center points of multivalent functions, Duke Math. J. 12 (1945), 669-684. MR 7, 379. MR 0015161 (7:379c)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288267-7
Keywords: Coefficients, starlike, meromorphic functions, univalent
Article copyright: © Copyright 1972 American Mathematical Society

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