### Abstract

The purpose of the present paper is to use the so-called pre-Schwarzian derivatives to obtain some properties of certain integral operator. We first establish the relationships between the two integral operators F_{n} and F_{γ1,...,γn}, which were given by Breaz and Breaz [1], and Breaz et. al [2] respectively, under the familiar classes of starlike of order α, S^{*}(α) and convex functions of order α, K(α). Furthermore, some other properties of the integral operator F_{γ1,...,γn} by using the concept of the norm and pre-Schwarzian derivatives are obtained.

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

Pages (from-to) | 2101-2109 |

Number of pages | 9 |

Journal | International Journal of Mathematical Analysis |

Volume | 4 |

Issue number | 41-44 |

Publication status | Published - 2010 |

### Fingerprint

### Keywords

- Analytic and univalent functions
- Convex functions
- Integral operators
- Pre-Shwarzian derivatives
- Starlike functions
- Uniformly locally univalent

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*International Journal of Mathematical Analysis*,

*4*(41-44), 2101-2109.

**New properties for certain integral operators.** / Mohammed, Aabed; Darus, Maslina.

Research output: Contribution to journal › Article

*International Journal of Mathematical Analysis*, vol. 4, no. 41-44, pp. 2101-2109.

}

TY - JOUR

T1 - New properties for certain integral operators

AU - Mohammed, Aabed

AU - Darus, Maslina

PY - 2010

Y1 - 2010

N2 - The purpose of the present paper is to use the so-called pre-Schwarzian derivatives to obtain some properties of certain integral operator. We first establish the relationships between the two integral operators Fn and Fγ1,...,γn, which were given by Breaz and Breaz [1], and Breaz et. al [2] respectively, under the familiar classes of starlike of order α, S*(α) and convex functions of order α, K(α). Furthermore, some other properties of the integral operator Fγ1,...,γn by using the concept of the norm and pre-Schwarzian derivatives are obtained.

AB - The purpose of the present paper is to use the so-called pre-Schwarzian derivatives to obtain some properties of certain integral operator. We first establish the relationships between the two integral operators Fn and Fγ1,...,γn, which were given by Breaz and Breaz [1], and Breaz et. al [2] respectively, under the familiar classes of starlike of order α, S*(α) and convex functions of order α, K(α). Furthermore, some other properties of the integral operator Fγ1,...,γn by using the concept of the norm and pre-Schwarzian derivatives are obtained.

KW - Analytic and univalent functions

KW - Convex functions

KW - Integral operators

KW - Pre-Shwarzian derivatives

KW - Starlike functions

KW - Uniformly locally univalent

UR - http://www.scopus.com/inward/record.url?scp=78650429246&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650429246&partnerID=8YFLogxK

M3 - Article

VL - 4

SP - 2101

EP - 2109

JO - International Journal of Mathematical Analysis

JF - International Journal of Mathematical Analysis

SN - 1312-8876

IS - 41-44

ER -