A new general idea for starlike and convex functions
DOI:
https://doi.org/10.5556/j.tkjm.47.2016.2157Keywords:
Analytic functions, Univalent functions, Starlike function of order $\alpha$, Convex function of order $\alpha$, Coefficient inequalities, General class of analytic functions.Abstract
Let $\mathcal{A}$ be the class of functions $f(z)$ which are analytic in the open unit disk $\mathbb{U}$ with $f(0)=0$ and $f'(0)=1$. For the class $\mathcal{A}$, a new general class $\mathcal{A}_{k}$ is defined. With this general class $\mathcal{A}_{k}$, two interesting classes $\mathcal{S}_{k}^{\ast}(\alpha)$ and $\mathcal{K}_{k}(\alpha)$ concerning classes of starlike of order $\alpha$ in $\mathbb{U}$ and convex of order $\alpha$ in $\mathbb{U}$ are considered.References
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