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Coefficient inequalities for concave and meromorphically starlike univalent functions

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Bhowmik B., Ponnusamy S.

Annales Polonici Mathematici

2008

tom 93

nr 2

177-186

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Bhowmik B.

1 Ponnusamy S.

1 2008

Wyniki wyszukiwania

Coefficient inequalities for concave and meromorphically starlike univalent functions