"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science
| Univalent functions and differential subordinations |
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| Teaching Staff in Charge |
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| Aims |
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The aim of this course is to realize a deep study of univalent functions, which are essential in geometric function theory. |
| Content |
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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 |
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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 |
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exam (70%) + home-work (30%) |