We study functions f(z) which are meromorphic and univalent in the unit disk with a simple pole at z = p, 0 < p < 1, and which map the unit disk onto a domain whose complement is either convex or is starlike with respect to a point w₀ ≠ 0.
@article{bwmeta1.element.bwnjournal-article-apmv59z3p275bwm,
author = {Albert E. Livingston},
title = {Convex meromorphic mappings},
journal = {Annales Polonici Mathematici},
volume = {60},
year = {1994},
pages = {275-291},
zbl = {0811.30010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv59z3p275bwm}
}
Albert E. Livingston. Convex meromorphic mappings. Annales Polonici Mathematici, Tome 60 (1994) pp. 275-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv59z3p275bwm/
[000] [1] L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152. | Zbl 0573.30014
[001] [2] A. W. Goodman, Functions typically-real and meromorphic in the unit circle, Trans. Amer. Math. Soc. 8 (1950), 92-105. | Zbl 0072.29302
[002] [3] J. A. Jenkins, On a conjecture of Goodman concerning meromorphic univalent functions, Michigan Math. J. 9 (1962), 25-27. | Zbl 0112.05102
[003] [4] W. E. Kirwan and G. Schober, Extremal problems for meromorphic univalent functions, J. Analyse Math. 30 (1976), 330-348. | Zbl 0343.30010
[004] [5] Y. Komatu, Note on the theory of conformal representation by meromorphic functions I, II, Proc. Japan Acad. 21 (1945), 269-284.
[005] [6] A. E. Livingston, The coefficients of multivalent close to convex functions, Proc. Amer. Math. Soc. 21 (1969), 545-552. | Zbl 0186.39901
[006] [7] J. Miller, Convex meromorphic mappings and related functions, Proc. Amer. Math. Soc. 25 (1970), 220-228.
[007] [8] J. Miller, Starlike meromorphic functions, Proc. Amer. Math. Soc. 31 (1972), 446-452. | Zbl 0235.30012
[008] [9] J. Miller, Convex and starlike meromorphic functions, Proc. Amer. Math. Soc. 80 (1980), 607-613. | Zbl 0451.30008
[009] [10] J. Pfaltzgraff and B. Pinchuk, A variational method for classes of meromorphic functions, J. Analyse Math. 24 (1971), 101-150. | Zbl 0247.30012
[010] [11] W. C. Royster, Convex meromorphic functions, in Mathematical Essays Dedicated to A. J. MacIntyre, Ohio Univ. Press, Athens, Ohio, 1970, 331-339. | Zbl 0211.09901
[011] [12] G. Schober, Univalent Functions - Selected Topics, Lecture Notes in Math. 478, Springer, Berlin, 1975. | Zbl 0306.30018