Faculty of Mathematics and Computer Science

Univalent functions and differential subordinations |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

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. |

References |

1. P. T. Mocanu, T. Bulboaca, G. S. Salagean, Teoria geometrica a functiilor univalente, Casa Cartii de Stiinta, Cluj-Napoca, 1999.
2. S. S. Miller, P. T. Mocanu, Differential Subordinations. Theory and Applications, Marcel Dekker Inc., New York – Basel, 2000 3. G. S. Salagean, Geometria planului complex, ProMedia Plus, Cluj-Napoca, 1997 4. I. Graham, G. Kohr, Geometric function theory in one and higher dimensions, Marcel Dekker, 2003. 5. A.W. Goodman, Univalent Functions, Mariner Publ.Comp., 1984. 6. P.L. Duren, Univalent Functions, Springer-Verlag, 1984. 7. Ch. Pommerenke, Univalent Functions, Gottingen, 1975. |

Assessment |

exam |