Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T00:24:04.971Z Has data issue: false hasContentIssue false
  • English
  • Français

Coefficient Estimates for a Class of Star-Like Functions

Published online by Cambridge University Press:  20 November 2018

D. A. Brannan ,
J. Clunie  and
W. E. Kirwan
D. A. Brannan
Affiliation:
Syracuse University, Syracuse, New York
J. Clunie
Affiliation:
Imperial College, London, England
W. E. Kirwan
Affiliation:
University of Maryland, College Park, Maryland
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 this note we continue the study, initiated in [1], of the class S*(α) of functions

(1.1)

that are analytic and univalent in the unit disc U and satisfy the condition

(1.2)

S*(1) is the frequently studied class of univalent star-like functions. For each α, S*(α) is a subclass of the class K(α) of close-to-convex functions of order α introduced by Pommerenke [4]. Properties of the class S*(α) proved useful in studying the coefficient behaviour of bounded univalent functions that are analytic and map U onto a convex domain [1]. In this note we investigate the problem of determining

but we are able to give only a partial solution.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 3 , 01 June 1970 , pp. 476 - 485
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Brannan, D. A. and Kirwan, W. E., On some classes of bounded univalent functions, J. London Math. Soc. (2) 1 (1969), 431–443.Google Scholar
2. Carathéodory, C., Uber der Variabilitdtsbereich der Fouriershen Konstanten von positiven harmonischen Functionen, Rend. Circ. Mat. Palermo 32 (1911), 193–217.Google Scholar
3. Clunie, J., On meromorphic schlict functions, J. London Math. Soc. 84 (1959), 215–216.Google Scholar
4. Ch., Pommerenke, On the coefficients of close-to-convex functions, Michigan Math. J. 9 (1962), 259–269.Google Scholar
5. Ch., Pommerenke, On meromorphic starlike functions, Pacific J. Math. 13 (1963), 221–235.Google Scholar
6. Rogosinski, W., On the coefficients of subordinate functions, Proc. London Math. Soc. 48 (1943), 48–82.Google Scholar
7. Rudin, W., Real and complex analysis (McGraw-Hill, New York, 1966).Google Scholar