Coefficient inequalities for concave and meromorphically starlike univalent functions

• Autorzy: B. Bhowmik , S. Ponnusamy
• Języki publikacji: EN

Abstrakty

EN

Let 𝔻 denote the open unit disk and f:𝔻 → ℂ̅ be meromorphic and univalent in 𝔻 with a simple pole at p ∈ (0,1) and satisfying the standard normalization f(0) = f'(0)-1 = 0. Also, assume that f has the expansion
$f(z) = ∑_{n=-1}^{∞} aₙ(z-p)ⁿ$, |z-p| < 1-p,
and maps 𝔻 onto a domain whose complement with respect to ℂ̅ is a convex set (starlike set with respect to a point w₀ ∈ ℂ, w₀ ≠ 0 resp.). We call such functions concave (meromorphically starlike resp.) univalent functions and denote this class by $Co(p)(Σ^{s}(p,w₀)$ resp.). We prove some coefficient estimates for functions in these classes; the sharpness of these estimates is also established.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2008
• Tom: 93
• Numer: 2
• Strony: 177-186

Daty

wydano

2008

Twórcy

autor

B. Bhowmik

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

autor

S. Ponnusamy

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

Identyfikatory

DOI

10.4064/ap93-2-6