Problems and Properties for p-Valent Functions Involving a New Generalized Differential Operator

Ala' Ali Amourah, Tariq Al-Hawary, Maslina Darus

Abstract

In this paper, a new differential operator $A_{p}^{n}f(z)$ defined in the openunit disc $U=\left\{ z\in\mathbb{C}:\left\vert z\right\vert <1\right\} $ is introduced. We then, using thisoperator and introduce a new subclass of analytic functions $G(\mu,\lambda,\alpha,\beta,b,p).$ Moreover, we discuss coefficient estimates, growth and distortion theorems and inclusion properties for the function $f$ belonging to the class $G_{n}(\mu,\lambda,\alpha,\beta,b,p)$.