- Hacettepe Journal of Mathematics and Statistics
- Vol: 45 Issue: 5
- Some starlikeness and convexity properties for two new $p$−valent integral operators
Some starlikeness and convexity properties for two new $p$−valent integral operators
Authors : Erhan Deniz, Esra Deniz, Nizami Mustafa
Pages : 1367-1378
View : 14 | Download : 7
Publication Date : 2016-10-01
Article Type : Research
Abstract :In this paper, we define two new general $p$−valent integral operators in the unit disc $U$ and obtain the properties of $p$−valent starlikeness and $p$−valent convexity of these integral operators of $p$−valent functions on some classes of $\beta$−uniformly $p$−valent starlike and $\beta$−uniformly $p$−valent convex functions of complex order and type α $(0 ≤\leq \alpha < p)$. As special cases, the properties of $p$−valent starlikeness and $p$−valent convexity of the operators $\int_{0}^{z} pt^{p-1} \left( \frac{f(t)}{t^p}\right)^\delta dt$ and $\int_{0}^{z} pt^{p-1} \left( \frac{g'(t)}{pt^{p-1}}\right)^\delta dt$ are given .Keywords : Analytic functions, Integral operators, $eta$−uniformly $p$−valent starlike and $eta$−uniformly $p$−valent convex functions, Complex order