A variational method for univalent functions connected with antigraphy

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

The paper is devoted to a class of functions analytic and univalent in the unit disk that are connected with an antigraphy

e^{i φ} \bar{ω} + i ρ e^{i \frac{φ}{2}}

. Variational formulas and Grunsky inequalities are derived. As an application there are given some estimations in the considered class of functions.

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