Sufficient conditions for starlike and convex functions

• Autorzy: S. Ponnusamy , P. Vasundhra
• Języki publikacji: EN

Abstrakty

EN

For n ≥ 1, let 𝓐 denote the class of all analytic functions f in the unit disk Δ of the form $f(z) = z + ∑_{k=2}^∞ a_kz^k$. For Re α < 2 and γ > 0 given, let 𝓟(γ,α) denote the class of all functions f ∈ 𝓐 satisfying the condition
|f'(z) - α f(z)/z + α - 1| ≤ γ, z ∈ Δ.
We find sufficient conditions for functions in 𝓟(γ,α) to be starlike of order β. A generalization of this result along with some convolution results is also obtained.

Kategorie tematyczne

• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
• 30C55: General theory of univalent and multivalent functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2007
• Tom: 90
• Numer: 3
• Strony: 277-288

Daty

wydano

2007

Twórcy

autor

S. Ponnusamy

• Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

autor

P. Vasundhra

• Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

Identyfikatory

DOI

10.4064/ap90-3-7