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Coefficient inequalities for concave and meromorphically starlike univalent functions

B. Bhowmik, S. 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...

Coefficient inequality for transforms of parabolic starlike and uniformly convex functions

D. Vamshee Krishna, B. Venkateswarlu, T. RamReddy (2014)

Annales mathématiques Blaise Pascal

The objective of this paper is to obtain sharp upper bound to the second Hankel functional associated with the k t h root transform f ( z k ) 1 k of normalized analytic function f ( z ) belonging to parabolic starlike and uniformly convex functions, defined on the open unit disc in the complex plane, using Toeplitz determinants.

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