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.
Analytic functions Integral operators $\beta$−uniformly $p$−valent starlike and $\beta$−uniformly $p$−valent convex functions Complex order
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Yayımlanma Tarihi | 1 Ekim 2016 |
Yayımlandığı Sayı | Yıl 2016 Cilt: 45 Sayı: 5 |