Differential Subordination and Convolution Techniques

Geometric Function Theory, a branch of Complex Analysis, is one of the most fascinating branches of Mathematical Analysis. In 1851, Riemann mapping theorem gave birth to the Geometric Function Theory that allows pure and applied mathematicians and engineers to reduce the simply-connected domains D problems to the special case of open unit disk. This book encompasses some new subclasses of analytic functions and their various properties in the unit disk E by using convolution and subordination techniques. We use the concepts of symmetrical points, Janowski functions and generalized concept of functions of bounded boundary rotation in order to define these analytic subclasses. Certain geometric properties of these classes such as arc-length problems, coefficient bounds, radius problems, inclusion results and rate of growth have also been studied. The investigations produce some innovative new results, most of which are best possible, remarkably unique and interesting and productive enough to be generalized to produce previously known results, by manipulating the parameters. The book is rich with pioneering ideas that can motivate and inspire many researchers working in this area.