Displaying similar documents to “Coefficient bounds for some subclasses of p-valently starlike functions”

Univalence, strong starlikeness and integral transforms

M. Obradović, S. Ponnusamy, P. Vasundhra (2005)

Annales Polonici Mathematici

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Let represent the class of all normalized analytic functions f in the unit disc Δ. In the present work, we first obtain a necessary condition for convex functions in Δ. Conditions are established for a certain combination of functions to be starlike or convex in Δ. Also, using the Hadamard product as a tool, we obtain sufficient conditions for functions to be in the class of functions whose real part is positive. Moreover, we derive conditions on f and μ so that the non-linear integral...

Sufficient conditions for starlike and convex functions

S. Ponnusamy, P. Vasundhra (2007)

Annales Polonici Mathematici

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

On products of starlike functions. I

Georgi Dimkov (1991)

Annales Polonici Mathematici

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We deal with functions given by the formula F ( z ) = z G ' ( z ) = z ∏ j = 1 n ( f j ( z ) / z ) a j where f j ( z ) are starlike of order α j and a j are complex constants. In particular, radii of starlikeness and convexity as well as orders of starlikeness and convexity are found.