### Abstract

In this paper, we obtain the order of convexity of the integral operator I αi, βi γ (f1,..., fn)(z) = { fzo γt γ-1 (f'1(t)) α1 (f1(t)/t)β1...(fn(t)/t)βndt}1/γ of analytic functions when γ = 1. Furthermore, we derive sufficient conditions for this operator when β1 = 1 -α 1;; i = 1,... ,n, to be analytic: and univalent in the open unit disk.

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

Pages (from-to) | 465-473 |

Number of pages | 9 |

Journal | Proceedings of the Jangjeon Mathematical Society |

Volume | 16 |

Issue number | 4 |

Publication status | Published - 2013 |

### Fingerprint

### Keywords

- Analytic and univalent functions
- Integral operator
- Starlike and convex functions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the Jangjeon Mathematical Society*,

*16*(4), 465-473.

**Convexity and univalency of general integral operator.** / Frasin, B. A.; Darus, Maslina; Arif, M.

Research output: Contribution to journal › Article

*Proceedings of the Jangjeon Mathematical Society*, vol. 16, no. 4, pp. 465-473.

}

TY - JOUR

T1 - Convexity and univalency of general integral operator

AU - Frasin, B. A.

AU - Darus, Maslina

AU - Arif, M.

PY - 2013

Y1 - 2013

N2 - In this paper, we obtain the order of convexity of the integral operator I αi, βi γ (f1,..., fn)(z) = { fzo γt γ-1 (f'1(t)) α1 (f1(t)/t)β1...(fn(t)/t)βndt}1/γ of analytic functions when γ = 1. Furthermore, we derive sufficient conditions for this operator when β1 = 1 -α 1;; i = 1,... ,n, to be analytic: and univalent in the open unit disk.

AB - In this paper, we obtain the order of convexity of the integral operator I αi, βi γ (f1,..., fn)(z) = { fzo γt γ-1 (f'1(t)) α1 (f1(t)/t)β1...(fn(t)/t)βndt}1/γ of analytic functions when γ = 1. Furthermore, we derive sufficient conditions for this operator when β1 = 1 -α 1;; i = 1,... ,n, to be analytic: and univalent in the open unit disk.

KW - Analytic and univalent functions

KW - Integral operator

KW - Starlike and convex functions

UR - http://www.scopus.com/inward/record.url?scp=84893192902&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893192902&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84893192902

VL - 16

SP - 465

EP - 473

JO - Proceedings of the Jangjeon Mathematical Society

JF - Proceedings of the Jangjeon Mathematical Society

SN - 1598-7264

IS - 4

ER -