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Coefficient inequalities for concave and meromorphically starlike univalent functions

B. BhowmikS. Ponnusamy — 2008

Annales Polonici Mathematici

Let denote the open unit disk and f: → ℂ̅ be meromorphic and univalent in 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 a ( z - p ) , |z-p| < 1-p, and maps 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 C o ( p ) ( Σ s ( p , w ) resp.). We prove some coefficient...

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