## On Convex Functions with Complex Order Through Bounded Boundary Rotation

Mathematics in Computer Science, cilt.13, ss.433-439, 2019 (Diğer Kurumların Hakemli Dergileri)  • Cilt numarası: 13 Konu: 3
• Basım Tarihi: 2019
• Doi Numarası: 10.1007/s11786-019-00405-8
• Dergi Adı: Mathematics in Computer Science
• Sayfa Sayıları: ss.433-439

#### Özet

Let F be the class of functions $f\left(z\right)=z+{a}_{2}{z}^{2}+\cdots$ which are analytic in $\mathcal{D}=\left\{z:|z|<1\right\}$ and satisfies the condition

$\begin{array}{r}1+\frac{1}{b}z\frac{{f}^{″}\left(z\right)}{{f}^{\prime }\left(z\right)}={p}_{t}\left(z\right),\left(b\ne 0,b\in \mathcal{C},z\in \mathcal{D}\right)\end{array}$

where ${p}_{t}\left(z\right)=\left(\frac{t}{4}+\frac{1}{2}\right){p}_{1}\left(z\right)-\left(\frac{t}{4}-\frac{1}{2}\right){p}_{2}\left(z\right)$$t\ge 2,{p}_{1}\left(z\right),{p}_{2}\left(z\right)\in \mathcal{P}$$\mathcal{P}$ is the class of analytic functions with the positive real part (Caratheodory class) then this function will be called convex function by means of bounded boundary rotation and denoted by K(tb). In this present paper, we will introduce this class and its some properties.