### Abstract

Let SL ^{*}(β) denote the class of all analytic functions f in the unit disc U with the normalization f(0) = f′(0) -1 = 0, and satisfying the condition (Equation presenet) Thus, zf′(z)/f(z) is the interior of the right half of the lemniscate of Bernoulli γ: (x ^{2} + y ^{2}) ^{2} - 2(1 - β)(x ^{2} - y ^{2}) = 0. The radii of β-convexity, β-starlikeness (and some of others) for f ∈ SL ^{*}(β) are determined.

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

Pages (from-to) | 471-476 |

Number of pages | 6 |

Journal | International Journal of Pure and Applied Mathematics |

Volume | 73 |

Issue number | 4 |

Publication status | Published - 2011 |

### Fingerprint

### Keywords

- Analytic functions
- Convex functions
- K-starlike functions
- Starlike functions
- Strongly starlike functions

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*International Journal of Pure and Applied Mathematics*,

*73*(4), 471-476.

**On radius problems in the class of univalent functions.** / Amer, Ahmed; Darus, Maslina.

Research output: Contribution to journal › Article

*International Journal of Pure and Applied Mathematics*, vol. 73, no. 4, pp. 471-476.

}

TY - JOUR

T1 - On radius problems in the class of univalent functions

AU - Amer, Ahmed

AU - Darus, Maslina

PY - 2011

Y1 - 2011

N2 - Let SL *(β) denote the class of all analytic functions f in the unit disc U with the normalization f(0) = f′(0) -1 = 0, and satisfying the condition (Equation presenet) Thus, zf′(z)/f(z) is the interior of the right half of the lemniscate of Bernoulli γ: (x 2 + y 2) 2 - 2(1 - β)(x 2 - y 2) = 0. The radii of β-convexity, β-starlikeness (and some of others) for f ∈ SL *(β) are determined.

AB - Let SL *(β) denote the class of all analytic functions f in the unit disc U with the normalization f(0) = f′(0) -1 = 0, and satisfying the condition (Equation presenet) Thus, zf′(z)/f(z) is the interior of the right half of the lemniscate of Bernoulli γ: (x 2 + y 2) 2 - 2(1 - β)(x 2 - y 2) = 0. The radii of β-convexity, β-starlikeness (and some of others) for f ∈ SL *(β) are determined.

KW - Analytic functions

KW - Convex functions

KW - K-starlike functions

KW - Starlike functions

KW - Strongly starlike functions

UR - http://www.scopus.com/inward/record.url?scp=84855885037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855885037&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84855885037

VL - 73

SP - 471

EP - 476

JO - International Journal of Pure and Applied Mathematics

JF - International Journal of Pure and Applied Mathematics

SN - 1311-8080

IS - 4

ER -