## Hokkaido Mathematical Journal

### A generalization of starlike functions of order alpha

#### Abstract

For every $q\in(0,1)$ and $0\le \alpha \lt 1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $\alpha$, on the open unit disk. We study this class of functions and explore some inclusion properties with the well-known class of starlike functions of order $\alpha$. The paper is also devoted to the discussion on the Herglotz representation formula for analytic functions $zf'(z)/f(z)$ when $f(z)$ is $q$-starlike of order $\alpha$. As an application we also discuss the Bieberbach conjecture problem for the $q$-starlike functions of order $\alpha$.

#### Article information

Source
Hokkaido Math. J., Volume 46, Number 1 (2017), 15-27.

Dates
First available in Project Euclid: 30 June 2017

https://projecteuclid.org/euclid.hokmj/1498788094

Digital Object Identifier
doi:10.14492/hokmj/1498788094

Mathematical Reviews number (MathSciNet)
MR3677873

Zentralblatt MATH identifier
1361.30017

#### Citation

AGRAWAL, Sarita; SAHOO, Swadesh Kumar. A generalization of starlike functions of order alpha. Hokkaido Math. J. 46 (2017), no. 1, 15--27. doi:10.14492/hokmj/1498788094. https://projecteuclid.org/euclid.hokmj/1498788094