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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 3, Pages 459-464

Integral means of certain class of analytic functions

Department of Mathematics, Changsha Communications Institute, Hunan, Changsha 410076, China

Received 20 June 1991; Revised 3 September 1992

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we discuss the following class of functions Sλ(α,β)={f(z):|f(z)g(z)1|<β|λf(z)g(z)+1|,zD}  where  0λ1,0<β1,0α<1, and f(z)=z+n=2anzn is analytic in D={z:|z|<1}, g(z) is a starlike function of order α. A subordination about this class is obtained, the integral means of functions in Sλ(α,β) and some extremal properties are studied.