On Certain Subclasses of Analytic Functions in Geometric Function Theory of a Complex Variable

Abstract

On Certain Subclasses of Analytic Functions in Geometric Function Theory of a Complex Variable In this thesis, we define some new subclasses of analytic functions using the techniques of convolution, differential subordination and the concepts of conic domains, bounded boundary rotation and bounded radius rotation. We study these new classes thoroughly and investigate several coefficient results, radii problems, convolution preserving properties, inclusion results, integral preserving mapping properties along with various other useful applications. Most of these results are sharp. Various known and new results are also derived as special cases from our results.