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On convex and starlike univalent functions

Published online by Cambridge University Press:  17 April 2009

R.K. Pandey  and
G.P. Bhargava
R.K. Pandey
Affiliation:
Department of Mathematics, PPN College, Kanpur - 208001, India.
G.P. Bhargava
Affiliation:
Department of Mathematics, PPN College, Kanpur - 208001, India.
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Abstract

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In this paper we obtain some classical results by using the general integral operators which transform Jakubowski's class K(m, M) into itself and K(μ) × S(m, M) into K(μ). Our results generalize some recent known results due to Causey and Reade, Patil and Thakare.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 3 , December 1983 , pp. 393 - 400
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Causey, W.M. and Reade, M.O., “On the univalence of functions defined by certain integral transforms”, J. Math. Anal. Appl. 89 (1982), 28–39.CrossRefGoogle Scholar
[2]Jakubowski, Z.J., “On the coefficients of starlike functions of some classes”, Ann. Polon. Math. 26 (1972), 305–313.CrossRefGoogle Scholar
[3]Patil, D.A. and Thakare, N.K., “On univalence of certain integrals”, Indian J. Pure Appl. Math. 11 (1980), 1626–1642.Google Scholar
[4]Robertson, M.S., “On the theory of univalent functions”, Ann. of Math. (2) 37 (1936), 374–408.CrossRefGoogle Scholar
[5]Shukla, S.L. and Kumar, V., “Jakubowski starlike integral operators”, J. Austral. Math. Soc. Ser. A (to appear).Google Scholar