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

• Autorzy: Richard Fournier
• Języki publikacji: EN

Abstrakty

EN

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 𝔻, and belonging to the class H = {f | f'(𝔻) lies in the right half-plane.} More generally let H* = {f | f'(𝔻) lies in some half-plane not containing 0.} To the best of our knowledge, the radii of starlikeness of both H and H* are still unknown, in spite of the fact that corresponding extremal functions can be described in a relatively simple way (by using, for example, Ruscheweyh's duality theory [15]). This paper is a survey of recent results concerning the radius of starlikeness of K = {f ∈ H | |f'(z)-1| < 1, z ∈ 𝔻}.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1995
• Tom: 31
• Numer: 1
• Strony: 187-195

Daty

wydano

1995

Twórcy

autor

Richard Fournier

• Département de Mathématiques et de Statistique, Université de Montréal, Montréal (QC) H3C 3J7, Canada

Bibliografia

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