1992•International Journal of Mathematics and Mathematical SciencesOpen access

Integral means of certain class of analytic functions

Gao Chunyi

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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.

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What this paper is about

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.

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Available 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.

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