2013•Journal of Sichuan Normal UniversityRequires access

On Certain Subclass of Analytic Functions Involving Salagean Operator

LI Xiao-fe

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Abstract

In this article,a new subclass Mm,n( α,β) = {f( z) : Re(Dmf( z)/Dnf( z)) β|Dmf( z)/Dnf( z)- 1 | + α( z∈U),α 1,β≤0,m∈N,n ∈N 0 } of univalent and analytic functions involving Salagean operator in the open disc U = { z: |z| 1} is introduced. The coefficients inequalities,distortion inequalities,extreme points and subordinating property are discussed by using solutions of inequalities tech- niques and theories of analytic functions. The sharp results are obtaind which generalize some know results.

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What this paper is about

In this article,a new subclass Mm,n( α,β) = {f( z) : Re(Dmf( z)/Dnf( z)) β|Dmf( z)/Dnf( z)- 1 | + α( z∈U),α 1,β≤0,m∈N,n ∈N 0 } of univalent and analytic functions involving Salagean operator in the open disc U = { z: |z| 1} is introduced. The coefficients inequalities,distortion inequalities,extreme points and subordinating property are discussed by using solutions of inequalities tech- niques and theories of analytic functions. The sharp results are obtaind which generalize some know results.

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Available abstract

In this article,a new subclass Mm,n( α,β) = {f( z) : Re(Dmf( z)/Dnf( z)) β|Dmf( z)/Dnf( z)- 1 | + α( z∈U),α 1,β≤0,m∈N,n ∈N 0 } of univalent and analytic functions involving Salagean operator in the open disc U = { z: |z| 1} is introduced. The coefficients inequalities,distortion inequalities,extreme points and subordinating property are discussed by using solutions of inequalities tech- niques and theories of analytic functions. The sharp results are obtaind which generalize some know results.

Key concepts: Subclass, Operator (biology), Mathematics, Distortion (music), Analytic function, Property (philosophy), Extreme point, Inequality

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