On a class of extremal quasi-conformal mappings
On a class of starlike functions defined in a halfplane
Let D = z: Re z < 0 and let S*(D) be the class of univalent functions normalized by the conditions , a a finite complex number, 0 ∉ f(D), and mapping D onto a domain f(D) starlike with respect to the exterior point w = 0. Some estimates for |f(z)| in the class S*(D) are derived. An integral formula for f is also given.
On a fundamental variational lemma for extremal quasiconformal mappings.
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.