Linear Operators and Related Topics in Geometric Function Theory

Abstract

The current thesis aims at studying linear operators and related topics in Geometric Function Theory. We describe various novel classes of analytic functions by using linear differential operator. Additionally, our focus is on studying subclasses of analytic, univalent and bi-univalent functions. We have studied and investigated some integral properties of aforementioned classes such as inclusion relations, convolution, extreme point and closure property, initial coefficients, upper bounds |𝑎𝑛|, sufficiency criteria, Fekete-Szego inequality and some other problems. We also deal with conic domains, and certain new classes of analytic functions representing conic domains have also been introduced. We have also discussed few applications of these operators which are associated with conic domains.