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Lobachevskii Journal of Mathematics, 2006, Volume 22, Pages 19–26
(Mi ljm41)
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This article is cited in 1 scientific paper (total 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.
Citation:
M. Darus, Kh. al-Shaqsi, “On harmonic univalent functions defined by a generalized Ruscheweyh derivatives operator”, Lobachevskii J. Math., 22 (2006), 19–26
Linking options:
https://www.mathnet.ru/eng/ljm41 https://www.mathnet.ru/eng/ljm/v22/p19
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Abstract page: | 606 | Full-text PDF : | 239 | References: | 58 |
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