Displaying similar documents to “Integral representations of bounded starlike functions”

On starlikeness of certain integral transforms

S. Ponnusamy (1992)

Annales Polonici Mathematici

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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.

Starlikeness of functions satisfying a differential inequality

Rosihan M. Ali, S. Ponnusamy, Vikramaditya Singh (1995)

Annales Polonici Mathematici

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In a recent paper Fournier and Ruscheweyh established a theorem related to a certain functional. We extend their result differently, and then use it to obtain a precise upper bound on α so that for f analytic in |z| < 1, f(0) = f'(0) - 1 = 0 and satisfying Re{zf''(z)} > -λ, the function f is starlike.

On a radius problem concerning a class of close-to-convex functions

Richard Fournier (1995)

Banach Center Publications

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The problem of estimating the radius of starlikeness of various classes of close-to-convex functions has attracted a certain number of mathematicians involved in geometric function theory ([7], volume 2, chapter 13). Lewandowski [11] has shown that normalized close-to-convex functions are starlike in the disc | z | < 4 √ 2 - 5 . Krzyż [10] gave an example of a function f ( z ) = z + ∑ n = 2 ∞ a n z n , non-starlike in the unit disc , and belonging to the class H = f | f’() lies in the right half-plane. More generally let H* = f |...

On a class of starlike functions defined in a halfplane

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

Annales Polonici Mathematici

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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.