On differential subordinations of multivalent functions involving a certain fractional derivative operator.
On discrepancy theorems with applications to approximation theory
We give an overview on discrepancy theorems based on bounds of the logarithmic potential of signed measures. The results generalize well-known results of P. Erdős and P. Turán on the distribution of zeros of polynomials. Besides of new estimates for the zeros of orthogonal polynomials, we give further applications to approximation theory concerning the distribution of Fekete points, extreme points and zeros of polynomials of best uniform approximation.
On Dittmar's approach to the Beltrami equation
We recall an old result of B. Dittmar. This result permits us to obtain an existence theorem for the Beltrami equation and some other results as a direct consequence of Moser's classical estimates for elliptic operators.
On Dyakonov type theorems for harmonic quasiregular mappings
We prove two Dyakonov type theorems which relate the modulus of continuity of a function on the unit disc with the modulus of continuity of its absolute value. The methods we use are quite elementary, they cover the case of functions which are quasiregular and harmonic, briefly hqr, in the unit disc.
On entire functions which transform straight lines into parabolas
On estimates of functionals in some classes of functions with positive real part
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 extremal problems related to inverse balayage.
On Extreme Bloch Functions with Prescribed Critical Points.
On Extreme Points of Families of Analytic Functions with Values in a Convex Set.
On finding the largest root of a polynomial
On folding solutions of the Beltrami equation.
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 generalized Pascu class of functions
On generators in ideals of entire functions of finite order and type on the plane.
On geometric convergence of discrete groups
One of the basic questions in the Kleinian group theory is to understand both algebraic and geometric limiting behavior of sequences of discrete subgroups. In this paper we consider the geometric convergence in the setting of the isometric group of the real or complex hyperbolic space. It is known that if is a non-elementary finitely generated group and a sequence of discrete and faithful representations, then the geometric limit of is a discrete subgroup of . We generalize this result by...
On geometrical properties of free boundaries in the Hele-Shaw flow moving boundary problem.
On growth of polynomials.