An application of Miller and Mocanu lemma

Let H[a_0,n] be the class of functions f(z)=a_0+a_nz^n+...which are analytic in the open unit disk U}. For f(z) in H[a_0,n], S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65(1978), 289-305) have shown Miller and Mocanu lemma which is the generalization of Jack lemma by I. S. Jack (J. London Ma...

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Bibliographic Details
Published in:arXiv.org 2013-03
Main Authors: Shiraishi, Hitoshi, Owa, Shigeyoshi
Format: Article
Language:English
Online Access:Get full text
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Summary:Let H[a_0,n] be the class of functions f(z)=a_0+a_nz^n+...which are analytic in the open unit disk U}. For f(z) in H[a_0,n], S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65(1978), 289-305) have shown Miller and Mocanu lemma which is the generalization of Jack lemma by I. S. Jack (J. London Math. Soc. 3(1971), 469-474). Applying Miller and Mocanu lemma, an interesting property for f(z) in H[a_0,n] and an example are discuss.
ISSN:2331-8422