On products of starlike functions. I

Georgi Dimkov

Georgi Dimkov

Annales Polonici Mathematici, Tome 55 (1991), p. 75-79 / Harvested from The Polish Digital Mathematics Library

Résumé

We deal with functions given by the formula $F (z) = z G^{'} (z) = z \prod_{j = 1}^{n} {(f_{j} (z) / z)}^{a_{j}}$ where $f_{j} (z)$ are starlike of order $α_{j}$ and $a_{j}$ are complex constants. In particular, radii of starlikeness and convexity as well as orders of starlikeness and convexity are found.

Publié le : 1991-01-01

Zbl 0769.30013

EUDML-ID : urn:eudml:doc:262235

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     title = {On products of starlike functions. I},
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     volume = {55},
     year = {1991},
     pages = {75-79},
     zbl = {0769.30013},
     language = {en},
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Georgi Dimkov. On products of starlike functions. I. Annales Polonici Mathematici, Tome 55 (1991) pp. 75-79. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p75bwm/

Bibliographie

[000] [1] H. Silverman, Products of starlike and convex functions, Ann. Univ. Mariae Curie-Skłodowska 29(1975), 109-116. | Zbl 0388.30010

[001] [2] A. W. Goodman, Univalent Functions, Mariner, 1983.