Abstract:
Some Subclasses of Analytic Functions Related with the
Generalizations of Functions with Bounded
Boundary Rotation
Geometric Function Theory on broad spectrum mostly deals with the geometric
properties of univalent, multivalent, meromorphic functions etc. and Theorists paid much
of their attention to the classes of these functions. Various subclasses of analytic
functions related with the Carathéodory functions along with their generalizations were
studied systematically in various aspects in the literature of the subject.
The main focus of this study is to define certain new subclasses of analytic functions
related with the functions of bounded boundary rotation and their generalizations. We use
the idea of convolution and subordination along with the concepts of bounded Mocanu
variation, Robertson functions, multiplier transformations etc. in defining these classes of
analytic as well as multivalent functions. We also investigate and explore these classes
and study various results like coefficient bounds, radius problems, inclusion results,
integral and convolution preserving properties etc. and their relationships with the
previously known results.
