Certain Subclasses of Analytic Functions Associated with Conic Domains

Abstract

Certain Subclasses of Analytic Functions Associated with Conic Domains Geometric Function Theory is the branch of Complex Analysis which deals with the study of geometric properties of analytic functions. While studying the geometric properties of analytic functions, we are mainly concerned with the geometry of image domains of analytic functions. On the basis of shape and other properties of image domain, analytic functions are categorized into many classes and then into subclasses. Only a few geometrical structures have been introduced as image domain in which conics is of great importance. The main focus of this study is to develop conic domains and to introduce some new geometrical structures as image domains. Our aim is to develop and refine already known conic domains and also to introduce certain new generalized domains and their associated functions. Also we deal with generalized circular domain and introduce certain new classes of analytic functions representing conic and circular domains simultaneously which is the main motivation of this work.