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On a class of starlike functions defined in a halfplane

G. Dimkov, J. Stankiewicz, Z. Stankiewicz (1991)

Annales Polonici Mathematici

Let D = z: Re z < 0 and let S*(D) be the class of univalent functions normalized by the conditions l i m D z ( f ( z ) - z ) = a , a a finite complex number, 0 ∉ f(D), and mapping D onto a domain f(D) starlike with respect to the exterior point w = 0. Some estimates for |f(z)| in the class S*(D) are derived. An integral formula for f is also given.

On a Convexity Preserving Integral Operator

Oros, Gheorghe, Irina Oros, Georgia (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 30C45, 30A20, 34C40In this paper we determine conditions an analytic function g needs to satisfy in order that the function Fgiven by (1) be convex.

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