On Some New Subclasses of Analytic Functions

Abstract

Geometric Function Theory is a branch of complex analysis which deals with the geometric properties of image domain of an analytic function and this research is rationalized with the advanced trends in this area. The main focus of this study is to define new subclasses of analytic functions using conic domains and Janowski functions. The technique of convolution and differential subordination is used to solve most of our results. We will use the concept of dual sets and quantum differential operator to study properties of these new subclasses. Some analytic and convolution properties such as inclusion results, radius problems and invariance under certain integral operators are studied. Several of the results are shown to be best possible. The connection of the results proved is established with already known ones.