Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T00:33:42.816Z Has data issue: false hasContentIssue false
  • English
  • Français

On Convex Univalent Functions

Published online by Cambridge University Press:  20 November 2018

T. Basgoze ,
J. L. Frank  and
F. R. Keogh
T. Basgoze
Affiliation:
Middle East Technical University, Ankara, Turkey
J. L. Frank
Affiliation:
University of Kentucky, Lexington, Kentucky
F. R. Keogh
Affiliation:
University of Kentucky, Lexington, Kentucky
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In what follows, we suppose that ƒ(z) = Σ0∞anzn is regular for |z| < 1. Let

and

Then (see, for example, [6, pp. 235-236]), for 0 ≦ r < ρ < 1, we have:

The following results are well known.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 1 , 01 February 1970 , pp. 123 - 127
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Clunie, J. and Keogh, F. R., On starlike and convex schlicht functions, J. London Math. Soc. 85 (1960), 229–233.Google Scholar
2. Hayman, W. K., Multivalent functions, Cambridge Tracts in Mathematics and Mathematical Physics, No. 48 (Cambridge Univ. Press, Cambridge, 1958).Google Scholar
3. Keogh, F. R., A strengthened form of the ¼theorem for starlike univalent functions (to appear in the A. J. Maclntyre Memorial Volume, Ohio Univ. Press).Google Scholar
4. Nehari, Z., Conformai mapping (McGraw-Hill, New York, 1952).Google Scholar
5. G., Pölya and I. J., Schoenberg, Remarks on de la Vallée Poussin means and convex conformai maps of the circle, Pacific J. Math. 8 (1958), 295–334.Google Scholar
6. Titchmarsh, E. C., The theory of functions, 2nd ed. (Oxford Univ. Press, London, 1939).Google Scholar