# On radius problems in the class of univalent functions

Ahmed Amer, Maslina Darus

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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 471-476 6 International Journal of Pure and Applied Mathematics 73 4 Published - 2011

### Fingerprint

Lemniscate of Bernoulli
Starlikeness
Univalent Functions
Unit Disk
Normalization
Convexity
Analytic function
Interior
Denote
Class

### Keywords

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

### ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

### Cite this

In: International Journal of Pure and Applied Mathematics, Vol. 73, No. 4, 2011, p. 471-476.

Research output: Contribution to journalArticle

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