On harmonic functions


Thesis Type: Doctorate

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

Approval Date: 2012

Thesis Language: Turkish

Student: ELİF YAŞAR

Supervisor: Sibel Yalçın Tokgöz

Abstract:

This study consists of four chapters.In the first chapter; basic definitions and theorems are given belong to the classes of analytic univalent, analytic p-valent, sense-preserving harmonic univalent, sense-preserving harmonic p-valent functions.In the second chapter; by using differential operator of Salagean, the classes of harmonic univalent functions with complex order are defined and relations between these classes are investigated. In addition, by using differential operator of Salagean, a new class of harmonic p-valent functions is defined and coefficient conditions and neighborhoods of the class in question are studied.In the third chapter; by using convolution of harmonic univalent functions and hypergeometric functions, two classes of harmonic univalent functions are defined and some properties, such as coefficient conditions and neighborhoods are investigated. In addition, a new operator which is obtained by using the convolution of harmonic p-valent functions and hypergeometric functions is defined. By using this operator, a new class of harmonic p-valent functions is defined and coefficient conditions, distortion bounds, extreme points are studied.In the fourth chapter; all obtained results are discussed.