### Abstract

The object of this paper is to show some properties of functions belonging to a subclass M (A, B,b,α) (where b is a complex number with R(b) >0,α > -1 and A,B are two arbitrary constants with (-1≤B <A <1). Coefficient estimates and some distortion theorems for this class of functions are found. Radii of close-to-convexity, starlikeness, convexity, convex linear combinations are derived. Therefore, interesting operators could be obtained with some earlier results using standard methods.

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

Pages (from-to) | 237-243 |

Number of pages | 7 |

Journal | Proceedings of the Pakistan Academy of Sciences |

Volume | 47 |

Issue number | 4 |

Publication status | Published - Dec 2010 |

### Keywords

- Analytic functions
- Close-to-convexity
- Linear combinations. AMS Mathematics Subject Classification:30C45
- Uniformly convex functions
- Uniformly starlike functions

### ASJC Scopus subject areas

- Social Sciences(all)

### Cite this

*Proceedings of the Pakistan Academy of Sciences*,

*47*(4), 237-243.

**Certain subclass of univalent analytic functions with negative coefficients of complex order.** / Ghanim, F.; Darus, Maslina.

Research output: Contribution to journal › Article

*Proceedings of the Pakistan Academy of Sciences*, vol. 47, no. 4, pp. 237-243.

}

TY - JOUR

T1 - Certain subclass of univalent analytic functions with negative coefficients of complex order

AU - Ghanim, F.

AU - Darus, Maslina

PY - 2010/12

Y1 - 2010/12

N2 - The object of this paper is to show some properties of functions belonging to a subclass M (A, B,b,α) (where b is a complex number with R(b) >0,α > -1 and A,B are two arbitrary constants with (-1≤B <A <1). Coefficient estimates and some distortion theorems for this class of functions are found. Radii of close-to-convexity, starlikeness, convexity, convex linear combinations are derived. Therefore, interesting operators could be obtained with some earlier results using standard methods.

AB - The object of this paper is to show some properties of functions belonging to a subclass M (A, B,b,α) (where b is a complex number with R(b) >0,α > -1 and A,B are two arbitrary constants with (-1≤B <A <1). Coefficient estimates and some distortion theorems for this class of functions are found. Radii of close-to-convexity, starlikeness, convexity, convex linear combinations are derived. Therefore, interesting operators could be obtained with some earlier results using standard methods.

KW - Analytic functions

KW - Close-to-convexity

KW - Linear combinations. AMS Mathematics Subject Classification:30C45

KW - Uniformly convex functions

KW - Uniformly starlike functions

UR - http://www.scopus.com/inward/record.url?scp=79953155282&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953155282&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79953155282

VL - 47

SP - 237

EP - 243

JO - Proceedings of the Pakistan Academy of Sciences

JF - Proceedings of the Pakistan Academy of Sciences

SN - 0377-2969

IS - 4

ER -