Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-12-03T19:11:48.769Z Has data issue: false hasContentIssue false
  • English
  • Français

Some applications of differential subordination

Published online by Cambridge University Press:  17 April 2009

K. S. Padmanabhan  and
R. Parvatham
K. S. Padmanabhan
Affiliation:
Ramanujan Institute, University of Madras, Madras – 600 005, India.
R. Parvatham
Affiliation:
Ramanujan Institute, University of Madras, Madras – 600 005, India.
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.

Let Sa (h) denote the class of analytic functions f on the unit disc E with f (0) =0 = f′ (0) −1 satisfying , where (a real), denotes the Hadamard product of Ka with f, and h is a convex univalent function on E, with Re h > 0. Let . It is proved that F ε Sa (h) whenever f ε Sa (h) and also that for a ≥ 1. Three more such classes are introduced and studied here. The method of differential subordination due to Eenigenburg et al. is used.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 3 , December 1985 , pp. 321 - 330
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Hassoon, S., Al-Amiri, , “Certain analogy of the α-convex functions”, Rev. Roum. Math. Pures et Appl. 23 (1978), 1449–1454.Google Scholar
[2]Chichra, P.N., “New subclasses of the class of close-to-convex functions”, Proc. Amer. Math. Soc. 62 (1977), 37–43.CrossRefGoogle Scholar
[3]Eenigenburg, P., Miller, S.S., Mocanu, P.T. and Reade, M.O., “On a Briot. Bouquet differential subordination”, General Inequalities 3 (1983), (Birkhauser Verlag–Basel), 339–348.Google Scholar
[4]Goel, R.M. and Mehrok, B.S., “Some invariance properties of a subclass of close-to-convex functions”, Indian J. Pure. Appl. Math., 12 (1981), 1240–1249.Google Scholar
[5]Kaplan, W., “Close-to-convex schlicht functions”, Michigan Math. J. 1 (1952), 169–185.CrossRefGoogle Scholar
[6]Libera, R.J., “Some classes of regular univalent functions”, Proc. Amer. Math. Soc. 16 (1965), 755–758.CrossRefGoogle Scholar
[7]Miller, S.S., Mocanu, P.T. and Reade, M.O., “All α-convex functions are univalent and starlike”, Proc. Amer. Math. Soc. 37 (1973), 553–554.Google Scholar
[8]St. Ruscheweyh, , “New criteria for univalent functions”, Proc. Amer. Math. Soc. 49 (1975), 109–115.CrossRefGoogle Scholar
[9]Zmorovich, V.A. and Pokhilevich, V.A., “On α-close-to-convex functions”, Ukrain. Mat. . 33 (1981), 670–673.Google Scholar