A variational method for univalent functions connected with antigraphy

• Autorzy: Janina Macura
• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to a class of functions analytic and univalent in the unit disk that are connected with an antigraphy $e^{iφ}\bar{ω} + iρe^{iφ/2}$. Variational formulas and Grunsky inequalities are derived. As an application there are given some estimations in the considered class of functions.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 37
• Numer: 1
• Strony: 21-28

Daty

wydano

1996

Twórcy

autor

Janina Macura

• Institute of Mathematics, Silesian Technical University, Kaszubska 23, PL-44-100 Gliwice, Poland

Bibliografia

• [1] R. Caccioppoli, Sui funzionali lineari nel campo delle funzioni analitiche, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 13 (1931), 263-266.
• [2] G. M. Goluzin, Geometričeskaya teorya funkcii kompleksnogo peremennogo, Moskwa 1966, 68-109, 157-158.
• [3] H. Jondro, Sur une méthode variationnelle dans la famille des fonctions de Grunsky-Shah, Bull. Acad. Polon. Sci. 27 (1979), 541-547.
• [4] H. Jondro, Les inégalités du type de Grunsky pour les fonctions de la classe K, Ann. Polon. Math. 45 (1985), 43-53.
• [5] G. Schober, Univalent functions, Selected Topics, Lecture Notes in Mathematics 478, Springer-Verlag 1975.