### Abstract

Let S_{H} denote the class of functions f = h + ḡ which axe harmonic univalent and sense preserving in the unit disk U. Al-Shaqsi and Darus[7] introduced a generalized Ruscheweyh derivatives operator 00 denoted by D_{λ}
^{n} where D_{λ}
^{n}(z) = z+ ∑_{k=2}
^{?∞}1 + λ(k - 1)]C(n, k)a _{k}z^{k}, where C(n, k) = (k+n-1 n). The authors, using this operators, introduce the class H_{λ}
^{n} of functions which are harmonic in U. Coefficient bounds, distortion bounds and extreme points are obtained.

Original language | English |
---|---|

Pages (from-to) | 19-26 |

Number of pages | 8 |

Journal | Lobachevskii Journal of Mathematics |

Volume | 22 |

Issue number | 1 |

Publication status | Published - 2006 |

### Fingerprint

### Keywords

- Derivative operator
- Harmonic functions
- Univalent functions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Lobachevskii Journal of Mathematics*,

*22*(1), 19-26.

**On harmonic univalent functions defined by a generalized Ruscheweyh derivatives operator.** / Darus, Maslina; Al Shaqsi, K.

Research output: Contribution to journal › Article

*Lobachevskii Journal of Mathematics*, vol. 22, no. 1, pp. 19-26.

}

TY - JOUR

T1 - On harmonic univalent functions defined by a generalized Ruscheweyh derivatives operator

AU - Darus, Maslina

AU - Al Shaqsi, K.

PY - 2006

Y1 - 2006

N2 - Let SH denote the class of functions f = h + ḡ which axe harmonic univalent and sense preserving in the unit disk U. Al-Shaqsi and Darus[7] introduced a generalized Ruscheweyh derivatives operator 00 denoted by Dλ n where Dλ n(z) = z+ ∑k=2 ?∞1 + λ(k - 1)]C(n, k)a kzk, where C(n, k) = (k+n-1 n). The authors, using this operators, introduce the class Hλ n of functions which are harmonic in U. Coefficient bounds, distortion bounds and extreme points are obtained.

AB - Let SH denote the class of functions f = h + ḡ which axe harmonic univalent and sense preserving in the unit disk U. Al-Shaqsi and Darus[7] introduced a generalized Ruscheweyh derivatives operator 00 denoted by Dλ n where Dλ n(z) = z+ ∑k=2 ?∞1 + λ(k - 1)]C(n, k)a kzk, where C(n, k) = (k+n-1 n). The authors, using this operators, introduce the class Hλ n of functions which are harmonic in U. Coefficient bounds, distortion bounds and extreme points are obtained.

KW - Derivative operator

KW - Harmonic functions

KW - Univalent functions

UR - http://www.scopus.com/inward/record.url?scp=33748298999&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748298999&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33748298999

VL - 22

SP - 19

EP - 26

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 1

ER -