Generalized problem of starlikeness for products of close-to-star functions

Jacek Dziok

Jacek Dziok

Annales Polonici Mathematici, Tome 107 (2013), p. 109-121 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider functions of the type $F (z) = z \prod_{j = 1}^{n} {[f_{j} (z) / z]}^{a_{j}}$ , where $a_{j}$ are real numbers and $f_{j}$ are $β_{j}$ -strongly close-to-starlike functions of order $α_{j}$ . We look for conditions on the center and radius of the disk (a,r) = z:|z-a| < r, |a| < r ≤ 1 - |a|, ensuring that F((a,r)) is a domain starlike with respect to the origin.

Publié le : 2013-01-01

Zbl 1276.30024

EUDML-ID : urn:eudml:doc:280756

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     author = {Jacek Dziok},
     title = {Generalized problem of starlikeness for products of close-to-star functions},
     journal = {Annales Polonici Mathematici},
     volume = {107},
     year = {2013},
     pages = {109-121},
     zbl = {1276.30024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-2-1}
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Jacek Dziok. Generalized problem of starlikeness for products of close-to-star functions. Annales Polonici Mathematici, Tome 107 (2013) pp. 109-121. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-2-1/