### Abstract

For 0, 0, we consider the M (, ) b of normalized analytic - convex functions defined in the open unit disc U. In this paper, we investigate the class M (, ) b, that is, Re { (z f b (z) / f b (z)) [ 1 - + (1 - ) (z f b (z) / f b (z)) + (1 + (z f b (z) / f b (z)))] } 0, with f b is Koebe type, that is, f b (z): = z / (1 - z n) b. The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class M (, ) b of n -fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.

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

Article number | 679704 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 2011 |

DOIs | |

Publication status | Published - 2011 |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

**Certain conditions for starlikeness of analytic functions of koebe type.** / Siregar, Saibah; Darus, Maslina.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Certain conditions for starlikeness of analytic functions of koebe type

AU - Siregar, Saibah

AU - Darus, Maslina

PY - 2011

Y1 - 2011

N2 - For 0, 0, we consider the M (, ) b of normalized analytic - convex functions defined in the open unit disc U. In this paper, we investigate the class M (, ) b, that is, Re { (z f b (z) / f b (z)) [ 1 - + (1 - ) (z f b (z) / f b (z)) + (1 + (z f b (z) / f b (z)))] } 0, with f b is Koebe type, that is, f b (z): = z / (1 - z n) b. The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class M (, ) b of n -fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.

AB - For 0, 0, we consider the M (, ) b of normalized analytic - convex functions defined in the open unit disc U. In this paper, we investigate the class M (, ) b, that is, Re { (z f b (z) / f b (z)) [ 1 - + (1 - ) (z f b (z) / f b (z)) + (1 + (z f b (z) / f b (z)))] } 0, with f b is Koebe type, that is, f b (z): = z / (1 - z n) b. The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class M (, ) b of n -fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.

UR - http://www.scopus.com/inward/record.url?scp=81755162027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=81755162027&partnerID=8YFLogxK

U2 - 10.1155/2011/679704

DO - 10.1155/2011/679704

M3 - Article

AN - SCOPUS:81755162027

VL - 2011

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

M1 - 679704

ER -