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 $\alpha$.
Citation
Sarita AGRAWAL. Swadesh Kumar SAHOO. "A generalization of starlike functions of order alpha." Hokkaido Math. J. 46 (1) 15 - 27, February 2017. https://doi.org/10.14492/hokmj/1498788094
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