Coefficient Estimates for Certain Subclasses of Analytic Functions Defined by New Differential Operator

Abstract

The study of operators plays an essential role in Mathematics, especially in Geometric Function Theory inComplex Analysis and its related fields. Many derivative and integral operators can be written in terms ofconvolution of certain analytic functions. The class of analytic functions, which has an essential place inthe theory of geometric functions, has been studied by many researchers before. This topic still maintainsits popularity today. In this paper, we investigate certain subclasses of analytic functions defined bygeneralized differential operators involving binomial series. Also, we obtain coefficient estimatesinvolving of the nonhomogeneous Cauchy-Euler differential equation of order 𝑟.Keywords: Analytic functions, coefficient bounds, differential operator, subordination.