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.
