Classes of analytic univalent function defined by differential operators


Thesis Type: Postgraduate

Institution Of The Thesis: Bursa Uludağ University, Fen Bilimleri Enstitüsü, Mathematics, Turkey

Approval Date: 2012

Thesis Language: Turkish

Student: YELİZ KARA

Supervisor: Sibel Yalçın Tokgöz

Abstract:

This work consist of three chapters. In the first chapter, some of concepts which will be used later are introduced. In the second chapter, basic properties of the class S of normalized functions by f(0)=f^' (0)-1=0 on E and of convex and starlike function classes which are the subclasses of S are, where E={z:|z|<1} is the unit disc. Furthermore area theorem for analytic, univalent functions on E^*={z:|z|>1} and a sharp upper bound for the second coefficient on S is obtained. In the last chapter, which consist of the main part of our study, on class of analytic, univalent functions defined by Salagean operator are introduced. In addition coefficient estimates, distortion theorems, extreme points are given.