"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Univalent Functions and Differential Subordinations
Code
Semes-
ter
Hours: C+S+L
Type
Section
MT255
1
2+1+1
compulsory
Analiza Reala si Complexa - în limba engleza
Teaching Staff in Charge
Prof. SALAGEAN Grigore Stefan, Ph.D.,  salageanmath.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.
References
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%)
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject