The Michigan Mathematical Journal

Poles near the origin produce lower bounds for coefficients of meromorphic univalent functions

F. G. Avkhadiev and K.-J. Wirths

Source: Michigan Math. J. Volume 52, Issue 1 (2004), 119-130.

Primary Subjects: 30C50
Secondary Subjects: 30C75

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.mmj/1080837738
Mathematical Reviews number (MathSciNet): MR2043400
Zentralblatt MATH identifier: 02114459
Digital Object Identifier: doi:10.1307/mmj/1080837738

References

F. G. Avkhadiev, Ch. Pommerenke, and K.-J. Wirths, On the coefficients of concave univalent functions, Math. Nachr., to appear.
Mathematical Reviews (MathSciNet): MR2068879
Digital Object Identifier: doi:10.1002/mana.200310177
F. G. Avkhadiev and K.-J. Wirths, Convex holes produce lower bounds for coefficients, Complex Variables Theory Appl. 47 (2002), 553--563.
Mathematical Reviews (MathSciNet): MR1918558
Digital Object Identifier: doi:10.1080/02781070290016223
A. Baernstein II and G. Schober, Estimates for inverse coefficients of univalent functions from integral means, Israel J. Math. 36 (1980), 75--82.
Mathematical Reviews (MathSciNet): MR589658
L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137--152.
Mathematical Reviews (MathSciNet): MR772434
Digital Object Identifier: doi:10.1007/BF02392821
C. Carathéodory, Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann. 64 (1907), 95--115.
Mathematical Reviews (MathSciNet): MR1511425
Digital Object Identifier: doi:10.1007/BF01449883
X. Fang, The distortion theorems and necessary and sufficient conditions of univalent meromorphic functions with $S(p),$ Acta Math. Sinica 28 (1985), 427--432.
Mathematical Reviews (MathSciNet): MR807231
W. Fenchel, Bemerkungen über die im Einheitskreis meromorphen schlichten Funktionen, Sitzungsber. Preussischen Akad. Wiss., Phys.-Math. Kl. 23 (1931), 431--436.
G. M. Goluzin, Geometric theory of functions of a complex variable, Transl. Math. Monog., 26, Amer. Math. Society, Providence, RI, 1969.
Mathematical Reviews (MathSciNet): MR247039
Zentralblatt MATH: 0183.07502
A. W. Goodman, Functions typically-real and meromorphic in the unit circle, Trans. Amer. Math. Soc. 81 (1956), 92--105.
Mathematical Reviews (MathSciNet): MR75299
Digital Object Identifier: doi:10.2307/1992854
------, Univalent functions, Mariner, Tampa, FL, 1983.
H. Grunsky, Neue Abschätzungen zur konformen Abbildung ein- und mehrfach zusammenhängender Bereiche, Schriftenreihe Math. Inst. und Inst. Angew. Math. Univ. Berlin 1 (1932), 95--140.
J. A. Jenkins, On a conjecture of Goodman concerning meromorphic univalent functions, Michigan Math. J. 9 (1962), 25--27.
Mathematical Reviews (MathSciNet): MR132170
Digital Object Identifier: doi:10.1307/mmj/1028998616
Project Euclid: euclid.mmj/1028998616
------, On meromorphic univalent functions, Complex Variables Theory Appl. 7 (1986), 83--87.
Mathematical Reviews (MathSciNet): MR877654
Y. Komatu, Note on the theory of conformal representation by meromorphic functions I and II, Proc. Japan Acad. 21 (1945 and 1949), 269--277 and 278--284.
Mathematical Reviews (MathSciNet): MR31564
Z. Lewandowski and E. Zlotkiewicz, On the domain of variability of the second coefficient for a class of meromorphic univalent functions, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 21--25.
Mathematical Reviews (MathSciNet): MR179345
R. J. Libera and A. E. Livingston, Weakly starlike meromorphic univalent functions, Trans. Amer. Math. Soc. 202 (1975), 181--191.
Mathematical Reviews (MathSciNet): MR361036
Digital Object Identifier: doi:10.2307/1997306
A. E. Livingston, Weakly starlike meromorphic univalent functions II, Proc. Amer. Math. Soc. 62 (1977), 43--45.
Mathematical Reviews (MathSciNet): MR435376
------, Convex meromorphic mappings, Ann. Polon. Math. 59 (1994), 275--291.
Mathematical Reviews (MathSciNet): MR1282779
K. Löwner, Untersuchungen über schlichte konforme Abbildungen des Einheitskreises I, Math. Ann. 89 (1923), 103--121.
Mathematical Reviews (MathSciNet): MR1512136
Digital Object Identifier: doi:10.1007/BF01448091
J. Miller, Convex and starlike meromorphic functions, Proc. Amer. Math. Soc. 80 (1980), 607--613.
Mathematical Reviews (MathSciNet): MR587937
Digital Object Identifier: doi:10.2307/2043433
Z. Nehari Conformal mapping, McGraw-Hill, New York, 1952.
Mathematical Reviews (MathSciNet): MR45823
Zentralblatt MATH: 0048.31503

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