g(z), where U(z) and g(z) are analytic in. We will introduced the operator Dn which defined by convolution involving the polylogarithms functions. Using this operator, we introduce the class HP(α,γ, n) by generalized derivative operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class HP(α,γ, n). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.'> g(z), where U(z) and g(z) are analytic in. We will introduced the operator Dn which defined by convolution involving the polylogarithms functions. Using this operator, we introduce the class HP(α,γ, n) by generalized derivative operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class HP(α,γ, n). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.'> g(z), where U(z) and g(z) are analytic in. We will introduced the operator Dn which defined by convolution involving the polylogarithms functions. Using this operator, we introduce the class HP(α,γ, n) by generalized derivative operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class HP(α,γ, n). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.'> g(z), where U(z) and g(z) are analytic in. We will introduced the operator Dn which defined by convolution involving the polylogarithms functions. Using this operator, we introduce the class HP(α,γ, n) by generalized derivative operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class HP(α,γ, n). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.'>
Paper title:

# On Certain Class of Harmonic Univalent Functions

Published in: Issue 1, (Vol. 6) / 2012
Publishing date: 2011-04-11
Pages: 54-59
Author(s): AL KASBI Nasser, DARUS Maslina
Abstract. A complex-valued functions that are univalent and sense preserving in the unit disk U can be written in the form f(z)= h(z)+ g(z), where U(z) and g(z) are analytic in. We will introduced the operator Dn which defined by convolution involving the polylogarithms functions. Using this operator, we introduce the class HP(α,γ, n) by generalized derivative operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class HP(α,γ, n). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.
Keywords: Univalent Functions, Harmonic Functions, Convex Combinations, Distortion Bounds
References:

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