On a Hölder type estimate for quasisymmetric functions
We give a Hölder type estimate for normalized ρ-quasisymmetric functions, improving some results of J. Zając.
On a Linear Combination of Some Expressions in the Theory of the Univalent Functions.
On a Mocanu type generalization of the Kaplan class K(α, β) of analytic functions
On a modification of the Poisson integral operator
Given a quasisymmetric automorphism γ of the unit circle T we define and study a modification Pγ of the classical Poisson integral operator in the case of the unit disk D. The modification is done by means of the generalized Fourier coefficients of γ. For a Lebesgue's integrable complex-valued function f on T, Pγ[f] is a complex-valued harmonic function in D and it coincides with the classical Poisson integral of f provided γ is the identity mapping on T. Our considerations are motivated by the...
On a Problem Concerning Harmonic Measure.
On a problem of Avhadiev.
On a Ruscheweyh type generalization of the Pascu class of analytic functions.
On an extremum problem in the class of mappings, quasiconformal in the mean.
On Analytic Self -Mappings of Riemann Surfaces II.
On Analytic Self-Mappings of Riemann Surfaces.
On bounded univalent functions that omit two given values
Let a,b ∈ z: 0<|z|<1 and let S(a,b) be the class of all univalent functions f that map the unit disk into {a,bwith f(0)=0. We study the problem of maximizing |f’(0)| among all f ∈ S(a,b). Using the method of extremal metric we show that there exists a unique extremal function which maps onto a simply connnected domain bounded by the union of the closures of the critical trajectories of a certain quadratic differential. If a<0
On certain classes of analytic functions
On conversion of the L'Hopital rule for analytic functions.
On convex univalent functions - II
On local injectivity and asymptotic linearity of quasiregular mappings
It is shown that the approximate continuity of the dilatation matrix of a quasiregular mapping f at implies the local injectivity and the asymptotic linearity of f at . Sufficient conditions for to behave asymptotically as are given. Some global injectivity results are derived.
On neighbourhoods of univalent starlike functions
On Nonvanishing Univalent Functions with Real Coefficients.
On one application of differential subordinations
On products of starlike functions. I
We deal with functions given by the formula where are starlike of order and are complex constants. In particular, radii of starlikeness and convexity as well as orders of starlikeness and convexity are found.
On -homeomorphisms.