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On starlikeness of certain integral transforms

S. Ponnusamy (1992)

Annales Polonici Mathematici

Let A denote the class of normalized analytic functions in the unit disc U = z: |z| < 1. The author obtains fixed values of δ and ϱ (δ ≈ 0.308390864..., ϱ ≈ 0.0903572...) such that the integral transforms F and G defined by F ( z ) = 0 z ( f ( t ) / t ) d t and G ( z ) = ( 2 / z ) 0 z g ( t ) d t are starlike (univalent) in U, whenever f ∈ A and g ∈ A satisfy Ref’(z) > -δ and Re g’(z) > -ϱ respectively in U.

On the extreme points of subordination families

Jacek Dziok (2010)

Annales Polonici Mathematici

We investigate extreme points of some classes of analytic functions defined by subordination and classes of functions with varying argument of coefficients. By using extreme point theory we obtain coefficient estimates and distortion theorems in these classes of functions. Some integral mean inequalities are also pointed out.

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