Classes of analytic univalent functions defined by convolution


Thesis Type: Postgraduate

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

Approval Date: 2016

Thesis Language: Turkish

Student: FİGEN EBREN CİHAN

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 Convolution are introduced. In addition coefficient estimates, distortion theorems, extreme points are given.