Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
MT255	Univalent Functions and Differential Subordinations	

Section	Semester	Hours: C+S+L	Category	Type	
Real and Compex Analysis - in English	1	2+1+1		compulsory	

Teaching Staff in Charge	Prof. SALAGEAN Grigore Stefan, Ph.D., salagean@math.ubbcluj.ro	
Aims	The aim of this course is to realize a deep study of univalent functions, which are essential in geometric function theory.	
Content	1. Univalent functions. Area Theorem. Covering and distortion theorems.
2. Holomorphic functions with positive real part. Herglotz formula. Integral representations. Subordination.
3. Classes of univalent functions. Starlike functions, convex functions, alpha-convex functions, spirallike functions, typically real functions. Meromorphic functions.
4. Differential subordinations. Fundamental lemmas. The class of admissible functions. Applications.
	
Bibliography	1. MOCANU, PETRU - BULBOACĂ, TEODOR - SĂLĂGEAN, GR. ŞTEFAN : Teoria geometrică a funcţiilor univalente, Cluj-Napoca: Casa Cărţii de Ştiinţă, 1999.
2. MILLER, SANDFORD S. - MOCANU, PETRU T. : Differential Subordinations. Theory and Applications, New York - Basel: Marcel Dekker Inc., 2000
3. POMMERENKE, CHRISTIAN : Univalent Functions, Göttingen: Vandenhoeck & Ruprecht,  1975
4. GOODMAN, WALTER A. : Univalent functions (vol. I, II), Tampa: Mariner Publishing Co., 1983.
5. GOLUZIN, GHENADII MIHAILOVICI : Geometric theory of functions of a complex variable, New York: Trans. Math. Mon., Amer. Math. Soc., 1969.
6. DUREN, PETER L. : Berlin, Heidelberg: Univalent functions, Springer Verlag,  1984.
7. BULBOACĂ, TEODOR - MOCANU, PETRU : Bevezetés az analitikus függvények geometriai elméletébe, Cluj-Napoca: Ed. Abel (Erdely Tankönyvtanács), 2003.
8. SĂLĂGEAN, GRIGORE STEFAN : Geometria planului complex, Cluj-Napoca: ProMedia Plus,  1997
9. GRAHAM, IAN - KOHR, GABRIELA : Geometric function theory in one and higher dimensions, New York: M. Dekker, 2003.	
Assessment	exam (70%) + home-work (30%)