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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.
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Abstract

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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

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