A Study on Differential Subordination

This book is a part of international research in geometric function theory. The book presents some applications of differential subordination and superordination for analytic functions in open unit disc on the complex plane which are associated with certain linear operators. Some of the results established in this book would provide extensions and improvements of those given in earlier works. The book consists of five chapters. First chapter is an introduction where we present some elementary concepts of univalent and p-valent functions, operators, subordination and superordination and preliminaries. Chapters 2 and 3 contains some applications of first order differential subordination, superordination and sandwich results for analytic functions involving certain linear operators. In chapters 4 and 5, making use of the results of Miller and Mocanu [ 53; Theorem 2:3b; p:28] and [ 54; Theorem 1; p: 818], certain classes of admissible functions are determined so that subordination as well as superordination implications of functions associated with the linear operators hold. Nine papers [12-20] have been extracted from this book.