Generalized Bazilevic and Related Functions

Abstract

In this thesis, we define and analyze some new classes related with generalized Bazilevic functions. We use different techniques and tools to introduce these classes including Robertson functions, integral operator, convolution operator, real and the complex order and differential subordination. These classes are thoroughly analyzed by studying their coefficient bounds, arc length problem, coefficient difference problem, integral representation, inclusion results, radius problems, maximum value of the modulus, the rate of Hankel determinant and Fekete Szego inequality of one of our defined class. We show that the class of generalized Bazilevic function is preserved under the Bernardi integral operator. The study of special cases for the different choices of parameter is also a part of our work. We establish a sound connection of our proved work with already existing results available in literature.