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 . Krzyż [10] gave an example of a function , 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 | f’() 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 ∈ .
@article{bwmeta1.element.bwnjournal-article-bcpv31z1p187bwm,
author = {Fournier, Richard},
title = {On a radius problem concerning a class of close-to-convex functions},
journal = {Banach Center Publications},
volume = {31},
year = {1995},
pages = {187-195},
zbl = {1107.30303},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p187bwm}
}
Fournier, Richard. On a radius problem concerning a class of close-to-convex functions. Banach Center Publications, Tome 31 (1995) pp. 187-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p187bwm/
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