TY - JOUR AU - Owa, Shigeyoshi AU - Mohan, Srivastava Hari AU - Hayami, Toshio AU - Kuroki, Kazuo PY - 2016/12/30 Y2 - 2024/03/28 TI - A new general idea for starlike and convex functions JF - Tamkang Journal of Mathematics JA - Tamkang J. Math. VL - 47 IS - 4 SE - Papers DO - 10.5556/j.tkjm.47.2016.2157 UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/2157 SP - 445-454 AB - 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. ER -