### Abstract

For analytic functions f normalized by f(0) = f0'(0) - 1 = 0 in the open unit disk U, a class Pα(λ) of f{hook} defined by{pipe}D^{α}
_{z}(z/f{hook}(z)){pipe} ≤, where D^{α}
_{z} denotes the fractional derivative of order α, m ≤ α < m + 1, m ε N0, is introduced. In this article, we study the problem when 1/r f{hook}(rz) ε Pα(λ), 3 ≤ α < 4.

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

Pages (from-to) | 55-58 |

Number of pages | 4 |

Journal | Matematicki Vesnik |

Volume | 63 |

Issue number | 1 |

Publication status | Published - 2011 |

### Fingerprint

### Keywords

- Analytic functions
- Cauchy-Schwarz inequality
- Fractional differential operator
- Univalent functions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Matematicki Vesnik*,

*63*(1), 55-58.

**Radius estimates of a subclass of univalent functions.** / Darus, Maslina; Ibrahim, Rabha W.

Research output: Contribution to journal › Article

*Matematicki Vesnik*, vol. 63, no. 1, pp. 55-58.

}

TY - JOUR

T1 - Radius estimates of a subclass of univalent functions

AU - Darus, Maslina

AU - Ibrahim, Rabha W.

PY - 2011

Y1 - 2011

N2 - For analytic functions f normalized by f(0) = f0'(0) - 1 = 0 in the open unit disk U, a class Pα(λ) of f{hook} defined by{pipe}Dα z(z/f{hook}(z)){pipe} ≤, where Dα z denotes the fractional derivative of order α, m ≤ α < m + 1, m ε N0, is introduced. In this article, we study the problem when 1/r f{hook}(rz) ε Pα(λ), 3 ≤ α < 4.

AB - For analytic functions f normalized by f(0) = f0'(0) - 1 = 0 in the open unit disk U, a class Pα(λ) of f{hook} defined by{pipe}Dα z(z/f{hook}(z)){pipe} ≤, where Dα z denotes the fractional derivative of order α, m ≤ α < m + 1, m ε N0, is introduced. In this article, we study the problem when 1/r f{hook}(rz) ε Pα(λ), 3 ≤ α < 4.

KW - Analytic functions

KW - Cauchy-Schwarz inequality

KW - Fractional differential operator

KW - Univalent functions

UR - http://www.scopus.com/inward/record.url?scp=78650612236&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650612236&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:78650612236

VL - 63

SP - 55

EP - 58

JO - Matematicki Vesnik

JF - Matematicki Vesnik

SN - 0025-5165

IS - 1

ER -