Some Subclasses of Analytic Functions Related with the Generalizations of Functions with Bounded Boundary Rotation

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.