- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 6
- Differential subordination and harmonic means for the Koebe type $n$-fold symmetric functions
Differential subordination and harmonic means for the Koebe type $n$-fold symmetric functions
Authors : Syed Zakar Hussain Bukhari, Maryam Nazir
Pages : 1630-1636
Doi:10.15672/hujms.1072813
View : 14 | Download : 5
Publication Date : 2022-12-01
Article Type : Research
Abstract :In this research, we develop some differential subordination results involving harmonic means of $f_{b}(z),f_{b}(z)+zf_{b}^{\prime}(z)$ and $f_{b}(z)+\frac{zf_{b}^{\prime}(z)}{f_{b}(z)},$ where $f_{b}(z)=\frac{z}{\left(1-z^{n}\right) ^{b}},$ $b\geq0;n\in\mathbb{N}=1,2,3...$ is an $n$-fold symmetric Koebe type functions defined in the unit disk with $f_{b}(0)=0,f_{b}^{\prime}(z)\neq0.$ By using the admissibility conditions, we also study several applications in the geometric function theory.Keywords : Differential subordination, harmonic means, Koebe type n-fold symmetric function