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

Jacek Dziok. "Generalized problem of starlikeness for products of close-to-star functions." Annales Polonici Mathematici 107.2 (2013): 109-121. <http://eudml.org/doc/280756>.

@article{JacekDziok2013,
abstract = {We consider functions of the type $F(z) = z∏_\{j=1\}^\{n\}[f_\{j\}(z)/z]^\{a_\{j\}\}$, 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.},
author = {Jacek Dziok},
journal = {Annales Polonici Mathematici},
keywords = {analytic functions; close-to-starlike functions; generalized starlikeness; radius of starlikeness},
language = {eng},
number = {2},
pages = {109-121},
title = {Generalized problem of starlikeness for products of close-to-star functions},
url = {http://eudml.org/doc/280756},
volume = {107},
year = {2013},
}

TY - JOUR
AU - Jacek Dziok
TI - Generalized problem of starlikeness for products of close-to-star functions
JO - Annales Polonici Mathematici
PY - 2013
VL - 107
IS - 2
SP - 109
EP - 121
AB - We consider functions of the type $F(z) = z∏_{j=1}^{n}[f_{j}(z)/z]^{a_{j}}$, 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.
LA - eng
KW - analytic functions; close-to-starlike functions; generalized starlikeness; radius of starlikeness
UR - http://eudml.org/doc/280756
ER -