Integral means of certain class of analytic functions

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.

Keywords

• analytic function
• subordination
• integral mean
• distortion
• coefficient inequality.