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On the univalent functions starlike with respect to a boundary point


Author: Pavel G. Todorov
Journal: Proc. Amer. Math. Soc. 97 (1986), 602-604
MSC: Primary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1986-0845972-9
MathSciNet review: 845972
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Abstract: For the examined functions, we have obtained a structure formula and estimates for $ \vert f(z)/(1 - z)\vert{\text{ }}$ and $ \vert\arg (f(z)/(1 - z))\vert$, the moduli of the partial sums of the coefficient series and the moduli of the coefficients.


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  • [1] M. S. Robertson, Univalent functions starlike with respect to a boundary point, J. Math. Anal. Appl. 81 (1981), 327-345. MR 622822 (82i:30017)
  • [2] A. Lyzzaik, On a conjecture of M. S. Robertson, Proc. Amer. Math. Soc. 91 (1984), 108-110. MR 735575 (85i:30018)
  • [3] C. Carathéodory, Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo 32 (1911), 193-217.
  • [4] G. M. Goluzin, Geometričeskaya teoriya funkcii kompleksnogo peremennogo, Izdanie vtoroe, Izdat. "Nauka", Moscow, 1966. MR 0219714 (36:2793)
  • [5] I. Ya. Asnevic and G. V. Ulina, Ob oblastyah znčienii analitčieskih funckcii, predstavimyh integralom Stil'tessa, Vestnik Leningrad. Univ. 10 (1955), 31-42. MR 0074515 (17:599d)
  • [6] M. S. Robertson, Quasi-subordinate functions, Mathematical Essays Dedicated to A. J. Macintyre, Ohio Univ. Press, Athens, Ohio, 1970, pp. 311-330. MR 0273004 (42:7885)
  • [7] -, On the theory of univalent functions, Ann. of Math. 37 (1936), 374-408. MR 1503286
  • [8] A. Schild, On starlike functions of order $ \alpha $, Amer. J. Math. 87 (1965), 65-70. MR 0174729 (30:4929)
  • [9] B. Pinchuk, On starlike and convex functions of order $ \alpha $,. Duke Math. J. 35 (1968), 72-734. MR 0230896 (37:6454)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0845972-9
Keywords: Univalent functions
Article copyright: © Copyright 1986 American Mathematical Society

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