## Tsukuba Journal of Mathematics

### Ruscheweyh derivative and strongly starlike functions

Liu Jinlin

#### Abstract

Let $A$ denote the class of analytic functions $f(z)$ defined in the unit disc satisfying the condition $f(O)=f^{\prime}(0)-1=0$. Let $\overline{S}^{*}(\beta, \gamma)$ be the class of strongly starlike functions of order $\beta$ and type $\gamma$, and let $\overline{C}(\beta, \gamma)$ denote the class of strongly convex functions of order $\beta$ and type $\gamma$. Certain new classes $\overline{S}_{\alpha}^{*}(\beta, \gamma)$ and $\overline{C}_{\alpha}(\beta, \gamma)$ are introduced by virtue of Ruscheweyh derivative and some properties of $\overline{S}_{\alpha}^{*}(\beta, \gamma)$ and $\overline{C}_{\alpha}(\beta, \gamma)$ are discussed.

#### Article information

Source
Tsukuba J. Math., Volume 24, Number 2 (2000), 303-309.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496164152

Digital Object Identifier
doi:10.21099/tkbjm/1496164152

Mathematical Reviews number (MathSciNet)
MR1818089

Zentralblatt MATH identifier
1009.30007

#### Citation

Jinlin, Liu. Ruscheweyh derivative and strongly starlike functions. Tsukuba J. Math. 24 (2000), no. 2, 303--309. doi:10.21099/tkbjm/1496164152. https://projecteuclid.org/euclid.tkbjm/1496164152