Convex meromorphic mappings

Albert E. Livingston

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 3, page 275-291
  • ISSN: 0066-2216

Abstract

top
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.

How to cite

top

Albert E. Livingston. "Convex meromorphic mappings." Annales Polonici Mathematici 59.3 (1994): 275-291. <http://eudml.org/doc/262315>.

@article{AlbertE1994,
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.},
author = {Albert E. Livingston},
journal = {Annales Polonici Mathematici},
keywords = {convex; starlike; meromorphic},
language = {eng},
number = {3},
pages = {275-291},
title = {Convex meromorphic mappings},
url = {http://eudml.org/doc/262315},
volume = {59},
year = {1994},
}

TY - JOUR
AU - Albert E. Livingston
TI - Convex meromorphic mappings
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 3
SP - 275
EP - 291
AB - 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.
LA - eng
KW - convex; starlike; meromorphic
UR - http://eudml.org/doc/262315
ER -

References

top
  1. [1] L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152. Zbl0573.30014
  2. [2] A. W. Goodman, Functions typically-real and meromorphic in the unit circle, Trans. Amer. Math. Soc. 8 (1950), 92-105. Zbl0072.29302
  3. [3] J. A. Jenkins, On a conjecture of Goodman concerning meromorphic univalent functions, Michigan Math. J. 9 (1962), 25-27. Zbl0112.05102
  4. [4] W. E. Kirwan and G. Schober, Extremal problems for meromorphic univalent functions, J. Analyse Math. 30 (1976), 330-348. Zbl0343.30010
  5. [5] Y. Komatu, Note on the theory of conformal representation by meromorphic functions I, II, Proc. Japan Acad. 21 (1945), 269-284. 
  6. [6] A. E. Livingston, The coefficients of multivalent close to convex functions, Proc. Amer. Math. Soc. 21 (1969), 545-552. Zbl0186.39901
  7. [7] J. Miller, Convex meromorphic mappings and related functions, Proc. Amer. Math. Soc. 25 (1970), 220-228. 
  8. [8] J. Miller, Starlike meromorphic functions, Proc. Amer. Math. Soc. 31 (1972), 446-452. Zbl0235.30012
  9. [9] J. Miller, Convex and starlike meromorphic functions, Proc. Amer. Math. Soc. 80 (1980), 607-613. Zbl0451.30008
  10. [10] J. Pfaltzgraff and B. Pinchuk, A variational method for classes of meromorphic functions, J. Analyse Math. 24 (1971), 101-150. Zbl0247.30012
  11. [11] W. C. Royster, Convex meromorphic functions, in Mathematical Essays Dedicated to A. J. MacIntyre, Ohio Univ. Press, Athens, Ohio, 1970, 331-339. Zbl0211.09901
  12. [12] G. Schober, Univalent Functions - Selected Topics, Lecture Notes in Math. 478, Springer, Berlin, 1975. Zbl0306.30018

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.