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

Banach Center Publications (1995)

- Volume: 31, Issue: 1, page 187-195
- ISSN: 0137-6934

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topFournier, Richard. "On a radius problem concerning a class of close-to-convex functions." Banach Center Publications 31.1 (1995): 187-195. <http://eudml.org/doc/262651>.

@article{Fournier1995,

abstract = {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 | 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 ∈ .},

author = {Fournier, Richard},

journal = {Banach Center Publications},

language = {eng},

number = {1},

pages = {187-195},

title = {On a radius problem concerning a class of close-to-convex functions},

url = {http://eudml.org/doc/262651},

volume = {31},

year = {1995},

}

TY - JOUR

AU - Fournier, Richard

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

JO - Banach Center Publications

PY - 1995

VL - 31

IS - 1

SP - 187

EP - 195

AB - 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 | 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 ∈ .

LA - eng

UR - http://eudml.org/doc/262651

ER -

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- [15] St. Ruscheweyh, Convolutions in Geometric Function Theory, Les Presses de l'Université de Montréal, Montréal, 1982.
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