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Function classes related to Ruscheweyh derivatives

Part of: Geometric function theory

Published online by Cambridge University Press:  09 April 2009

O. P. Ahuja  and
H. Silverman
O. P. Ahuja
Affiliation:
Department of Mathematics, University of Papua New GuineaPapua, New Guinea
H. Silverman
Affiliation:
Department of Mathematics, College of Charleston Charleston, South Carolina 29424, U.S.A.
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Abstract

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We investigate a family consisting of functions whose convolution with is starlike of order α 0 ≤ α < 1. We determine extreme points, inclusion relations, and show how this family acts under various linear operators.

MSC classification

Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 30C55: General theory of univalent and multivalent functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 3 , December 1989 , pp. 438 - 444
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Ahuja, O. P., ‘Integral operators of certain univalent functions’, Internal. J. Math. Sci. 8 (4) 1985, 653–662.CrossRefGoogle Scholar
[2]Ahuja, O. P., ‘On the radius problem of certain analytic functions’, Bull Korean Math. Soc. 22 (1) 1985, 31–36.Google Scholar
[3]Brickman, L., Hallenbeck, D. J., MacGregor, T. H., and Wilken, D. R., ‘Convex hulls and extreme points of families of starlike and convex mappings’, Trans. Amer. Math. Soc. 185 (1973), 413–428.CrossRefGoogle Scholar
[4]Ruscheweyh, S., ‘New criteria for univalent functions,’ Proc. Amer. Math. Soc. 49 (1975), 109–115.CrossRefGoogle Scholar
[5]Ruscheweyh, S., and Sheil-Small, T., ‘Hadamard products of schlicht functions and the Pólya-Schoenberg conjecture’, Comment. Math. Helv. 48 (1973), 119–135.CrossRefGoogle Scholar
[6]Silverman, H., ‘Univalent functions with negative coefficients’, Proc. Amer. Math. Soc. 51 (1975), 109–116.CrossRefGoogle Scholar
[7]Silverman, H., Silvia, E. M., and Telage, D. N., ‘Convolution conditions for convexity, star-likeness, and spiral-likeness’, Math. Z. 162 (1978), 125–130.CrossRefGoogle Scholar
[8]Singh, R. and Singh, S., ‘Integrals of certain univalent functions’, Proc. Amer. Math. Soc. 77 (1979), 336–343.CrossRefGoogle Scholar
[9]Suffridge, T. J., ‘Starlike functions as limits of polynomials’, Advances in Complex Function Theory, pp. 164–202, (Lecture Notes in Math. 505, Springer, 1976).CrossRefGoogle Scholar