Convex meromorphic mappings

Albert Livingston

ArticleOriginal scientific text

Title

Convex meromorphic mappings

Authors ¹

Affiliations

Department of Mathematical Sciences University of Delaware 501 Ewing Hall Newark, Delaware 19716 U.S.A.

Abstract

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.

Keywords

ENG

convex, starlike, meromorphic

L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152.
A. W. Goodman, Functions typically-real and meromorphic in the unit circle, Trans. Amer. Math. Soc. 8 (1950), 92-105.
J. A. Jenkins, On a conjecture of Goodman concerning meromorphic univalent functions, Michigan Math. J. 9 (1962), 25-27.
W. E. Kirwan and G. Schober, Extremal problems for meromorphic univalent functions, J. Analyse Math. 30 (1976), 330-348.
Y. Komatu, Note on the theory of conformal representation by meromorphic functions I, II, Proc. Japan Acad. 21 (1945), 269-284.
A. E. Livingston, The coefficients of multivalent close to convex functions, Proc. Amer. Math. Soc. 21 (1969), 545-552.
J. Miller, Convex meromorphic mappings and related functions, Proc. Amer. Math. Soc. 25 (1970), 220-228.
J. Miller, Starlike meromorphic functions, Proc. Amer. Math. Soc. 31 (1972), 446-452.
J. Miller, Convex and starlike meromorphic functions, Proc. Amer. Math. Soc. 80 (1980), 607-613.
J. Pfaltzgraff and B. Pinchuk, A variational method for classes of meromorphic functions, J. Analyse Math. 24 (1971), 101-150.
W. C. Royster, Convex meromorphic functions, in Mathematical Essays Dedicated to A. J. MacIntyre, Ohio Univ. Press, Athens, Ohio, 1970, 331-339.
G. Schober, Univalent Functions - Selected Topics, Lecture Notes in Math. 478, Springer, Berlin, 1975.

Title

Convex meromorphic mappings

Affiliations

Abstract

Keywords

Bibliography