International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 459-464
doi:10.1155/S0161171293000572
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 Gao Chunyi. 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.
Abstract
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|,z∈D} where 0≤λ≤1,0<β≤1,0≤α<1,
and f(z)=z+∑n=2∞anzn 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.