An Application of the Ruscheweyh Derivatives II
Publications de l'Institut Mathématique, _N_S_38 (1985) no. 52, p. 99
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
We introduce the class $R(\alpha)$ of functions of the form
$
f(z)= z- \sum_{k=2}^\infty a_kz^k \qquad (a_k\geq 0)
$
satisfying the condition
$
\text{Re}\{D^{\alpha+1}f(z)/D^\alpha f(z)\}>\alpha/(\alpha+1)
$
for some $(\alpha\geq 0)$ and for all $z\in U=\{z: |z| 1\}$, where
$D^\alpha f(z)$ denotes the Hadamard product of $z/(1-z)^{\alpha+1}$ and
$f(z)$. The object of the present paper is to prove some distortion and
closure theorems for functions $f(z)$ in $R(\alpha)$, and to give the result
for the modified Hadamard product of functions $f(z)$ belonging to the class
$R(\alpha)$. Furthermore, we determine the radii of starlikeness and
convexity of functions $f(z)$ in the class $R(\alpha)$.
Classification :
26A24 30C45
@article{PIM_1985_N_S_38_52_a14,
author = {Shigeyoshi Owa},
title = {An {Application} of the {Ruscheweyh} {Derivatives} {II}},
journal = {Publications de l'Institut Math\'ematique},
pages = {99 },
publisher = {mathdoc},
volume = {_N_S_38},
number = {52},
year = {1985},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1985_N_S_38_52_a14/}
}
Shigeyoshi Owa. An Application of the Ruscheweyh Derivatives II. Publications de l'Institut Mathématique, _N_S_38 (1985) no. 52, p. 99 . http://geodesic.mathdoc.fr/item/PIM_1985_N_S_38_52_a14/