On the Class of Analytic and Univalent Functions Defined by Differential Operator

Abstract

The main object of this article is to introduce a subclass A ( α , β , μ , τ ) consisting of analytic and univalent functions in the open unit disk. We investigative the coefficient bound, growth and distortion theorem for this class. Furthermore, we obtain convolutions property, convex linear combination and extreme point for these functions.

Bi-Univalent Function Classes Defined by Using an Einstein Function and a New Generalised Operator

“…Then, by inserting certain functions for 𝜙 in S * (𝜙), we obtain various subclasses of A with distinct geometric analyses, such as those from the work by Janowski (1970) , Mendiratta et al (2015) , and Cho et al (2019) . Many characteristics of the analytic univalent functions are connected with differential and integral operators, such as coefficient bound, covering theorems, distortion theorems, growth theorems, inclusion properties, and radius of convexity; all of these have been investigated (Omar and Abdul Halim, 2012;Zhang et al, 2021;Saheb and Al-Khafaji, 2021;Kumar and Sahoo, 2021;Awasthi, 2017). Yet, there has been relatively little research and discovery on the relevant features involving bi-univalent function subclasses.…”