Geodesic
On harmonic univalent functions defined by a~generalized Ruscheweyh derivatives operator
Lobachevskii journal of mathematics, Tome 22 (2006), pp. 19-26

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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. 
@article{LJM_2006_22_a2,
     author = {M. Darus and Kh. al-Shaqsi},
     title = {On harmonic univalent functions defined by a~generalized {Ruscheweyh} derivatives operator},
     journal = {Lobachevskii journal of mathematics},
     pages = {19--26},
     publisher = {mathdoc},
     volume = {22},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2006_22_a2/}
}
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M. Darus; Kh. al-Shaqsi. On harmonic univalent functions defined by a~generalized Ruscheweyh derivatives operator. Lobachevskii journal of mathematics, Tome 22 (2006), pp. 19-26. http://geodesic.mathdoc.fr/item/LJM_2006_22_a2/