Differential subordination and harmonic means for the Koebe type $n$-fold symmetric functions

Authors : Syed Zakar HUSSAİN BUKHARİ, Maryam NAZİR

Pages : 1630-1636

Doi:10.15672/hujms.1072813

View : 21 | Download : 9

Publication Date : 2022-12-01

Article Type : Research Paper

Abstract :In this research, we develop some differential subordination results involving harmonic means of $f_{b}insert ignore into journalissuearticles values(z);,f_{b}insert ignore into journalissuearticles values(z);+zf_{b}^{\prime}insert ignore into journalissuearticles values(z);$ and $f_{b}insert ignore into journalissuearticles values(z);+\frac{zf_{b}^{\prime}insert ignore into journalissuearticles values(z);}{f_{b}insert ignore into journalissuearticles values(z);},$ where $f_{b}insert ignore into journalissuearticles values(z);=\frac{z}{\leftinsert ignore into journalissuearticles values(1-z^{n}\right); ^{b}},$ $b\geq0;n\in\mathbb{N}=1,2,3...$ is an $n$-fold symmetric Koebe type functions defined in the unit disk with $f_{b}insert ignore into journalissuearticles values(0);=0,f_{b}^{\prime}insert ignore into journalissuearticles values(z);\neq0.$ 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