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JOURNALS // Lobachevskii Journal of Mathematics // Archive

Lobachevskii J. Math., 2006 Volume 22, Pages 19–26 (Mi ljm41)

This article is cited in 1 paper

On harmonic univalent functions defined by a generalized Ruscheweyh derivatives operator

M. Darus, Kh. al-Shaqsi

Universiti Kebangsaan Malaysia

Abstract: Let $\mathcal{S_H}$ denote the class of functions $f=h+\overline g$ which are harmonic univalent and sense preserving in the unit disk $\mathbf U$. Al-Shaqsi and Darus [7] introduced a generalized Ruscheweyh derivatives operator denoted by $D^n_\lambda$ where $D^n_\lambda f(z)=z+\sum\limits_{k=2}^\infty[1+\lambda(k-1)]C(n,k)a_kz^k$, where $C(n,k)={{k + n-1}\choose n}$. The authors, using this operators, introduce the class $\mathcal H^n_\lambda$ of functions which are harmonic in $\mathbf U$. Coefficient bounds, distortion bounds and extreme points are obtained.

Keywords: univalent functions, Harmonic functions, derivative operator.

Submitted by: M. A. Malakhaltsev
Received: 30.03.2006

Language: English



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