Some starlikeness and convexity properties for two new $p$−valent integral operators

Authors : Erhan DENİZ, Esra DENİZ, Nizami MUSTAFA

Pages : 1367-1378

View : 62 | Download : 12

Publication Date : 2016-10-01

Article Type : Research Paper

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 $insert ignore into journalissuearticles values(0 ≤\leq \alpha < p);$. As special cases, the properties of $p$−valent starlikeness and $p$−valent convexity of the operators $\int_{0}^{z} pt^{p-1} \leftinsert ignore into journalissuearticles values( \frac{finsert ignore into journalissuearticles values(t);}{t^p}\right);^\delta dt$ and $\int_{0}^{z} pt^{p-1} \leftinsert ignore into journalissuearticles values( \frac{g`insert ignore into journalissuearticles values(t);}{pt^{p-1}}\right);^\delta dt$   are given .
Keywords : Analytic functions, Integral operators, eta uniformly p valent starlike and eta uniformly p valent convex functions, Complex order

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