Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-16T17:13:43.720Z Has data issue: false hasContentIssue false
  • English
  • Français

Certain generalizations of presetarlike functions

Part of: Geometric function theory

Published online by Cambridge University Press:  09 April 2009

H. S. Al-Amiri
H. S. Al-Amiri
Affiliation:
Browling Green State UniversityBrowling Green, Ohio 43403, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

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.

The classes of prestarlike functions Rα, α ≧ – 1, were studied recently by St. Ruscheweyh. The author generalizes and extends these classes. In particular the author obtains the radius of Ra+1 for the class Rα, α ≧ –1.

Keywords

Univalent functionsprestarlike functionHadamard product.

MSC classification

Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 3 , November 1979 , pp. 325 - 334
Copyright
Copyright © Australian Mathematical Society 1979

References

Al-Amiri, H. S. (1978), ‘Certain analogy of the a-convex functions’, Rev. Roumaine Math. Pares Appl. 23, 1449–1454.Google Scholar
Jack, I. S. (1971), ‘Functions starlike and convex of order α’, J. London Math. Soc. (2) 3, 469–474.CrossRefGoogle Scholar
Kaplan, W. (1952), ‘Close-to-convex schlicht functions’, Michigan Math. J. 1, 169–185.CrossRefGoogle Scholar
Libera, R. J. (1965), ‘Some classes of regular univalent functions’, Proc. Amer. Math. Soc. 16, 755–758.CrossRefGoogle Scholar
Livingston, A. E. (1966), ‘On the radius of univalence of certain analytic functions’, Proc. Amer. Math. Soc. 17, 352–357.CrossRefGoogle Scholar
MacGregor, T. (1963), ‘The radius of convexity for starlike functions of order ½’, Proc. Amer. Math. Soc. 14, 71–76.Google Scholar
Mocanu, P. (1969), ‘Une propriété de convexité généralisée dans la représentation conforme’, Mathematica (Cluj) 11, 127–133.Google Scholar
Robertson, M. S. (1963), ‘Extremal problems for analytic functions with positive real part and applications’, Trans. Amer. Math. Soc. 106, 236–253.CrossRefGoogle Scholar
Ruscheweyh, S. (1975), ‘New criteria for univalent functions’, Proc. Amer. Math. Soc. 49, 109–115.CrossRefGoogle Scholar
Ruscheweyh, S. (1977), ‘Linear operators between classes of prestarlike functions’, Comm. Math. Helv. 52, 497–509.CrossRefGoogle Scholar
Suffridge, T. J. (1976), ‘Starlike functions as limits of polynomials’, Advances in complex function theory, pp. 164–202 (Lecture Notes in Mathematics 505, Springer-Verlag, Berlin).CrossRefGoogle Scholar
Zmorovič, V. A. (1969), ‘On bounds of convexity for starlike functions of order α in the circle ∥ z ∥ < 1 and the circular region 0< ∥z∥; <1,’, Amer. Math. Soc. Transl. (2) 80, 203–213.Google Scholar