On a Mocanu type generalization of the Kaplan class K(α, β) of analytic functions
On an extremal problem
Let denote the class of functions univalent and holomorphic in the unit disc . In the paper we obtain a sharp estimate of the functional in the class for an arbitrary .
On certain classes of analytic functions
On estimating a fifth order functional for bounded univalent functions
On estimating some initial inverse coefficients for meromorphic univalent functions omitting a disc.
On extremal mappings in complex ellipsoids
Using a generalization of [Pol] we present a description of complex geodesics in arbitrary complex ellipsoids.
On functions satisfying more than one equation of Schiffer type
The paper concerns properties of holomorphic functions satisfying more than one equation of Schiffer type (-equation). Such equations are satisfied, in particular, by functions that are extremal (in various classes of univalent functions) with respect to functionals depending on a finite number of coefficients.
On the characteristic properties of certain optimization problems in complex analysis
We shall be concerned in this paper with an optimization problem of the form: J(f) → min(max) subject to f ∈ 𝓕 where 𝓕 is some family of complex functions that are analytic in the unit disc. For this problem, the question about its characteristic properties is considered. The possibilities of applications of the results of general optimization theory to such a problem are also examined.
On the coefficients of bounded real univalent functions
On the existence of Jenkins-Strebel differentials using harmonic maps from surfaces to graphs.
On the univalent, bounded, non-vanishing and symmetric functions in the unit disk
The paper is devoted to a class of functions analytic, univalent, bounded and non-vanishing in the unit disk and in addition, symmetric with respect to the real axis. Variational formulas are derived and, as applications, estimates are given of the first and second coefficients in the considered class of functions.