O funkcích prostých
Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian
The relation between the Jacobian and the orders of a linear invariant family of locally univalent harmonic mapping in the plane is studied. The new order (called the strong order) of a linear invariant family is defined and the relations between order and strong order are established.
On a certain class of harmonic multivalent functions.
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 convolution conjecture of bounded functions.
On a generalization of close-to-convex functions
The paper of M. Ismail et al. [Complex Variables Theory Appl. 14 (1990), 77-84] motivates the study of a generalization of close-to-convex functions by means of a q-analog of the difference operator acting on analytic functions in the unit disk 𝔻 = {z ∈ ℂ:|z| < 1}. We use the term q-close-to-convex functions for the q-analog of close-to-convex functions. We obtain conditions on the coefficients of power series of functions analytic in the unit disk which ensure that they generate functions in...
On a Linear Combination of Some Expressions in the Theory of the Univalent Functions.
On an asymptotically sharp variant of Heinz's inequality.
On boundary correspondence under quasiconformal mappings.
On certain subclasses of bounded univalent functions
Let = z ∈ ℂ; |z| < 1, T = z ∈ ℂ; |z|=1. Denote by S the class of functions f of the form f(z) = z + a₂z² + ... holomorphic and univalent in , and by S(M), M > 1, the subclass of functions f of the family S such that |f(z)| < M in . We introduce (and investigate the basic properties of) the class S(M,m;α), 0 < m ≤ M < ∞, 0 ≤ α ≤ 1, of bounded functions f of the family S for which there exists an open of length 2πα such that for every and for every .
On certain univalence criteria
On locally biholomorphic mappings from multi-connected onto simply connected domains
We continue E. Ligocka's investigations concerning the existence of m-valent locally biholomorphic mappings from multi-connected onto simply connected domains. We decrease the constant m, and also give the minimum of m in the case of mappings from a wide class of domains onto the complex plane ℂ.
On locally biholomorphic surjective mappings
We prove that each open Riemann surface can be locally biholomorphically (locally univalently) mapped onto the whole complex plane. We also study finite-to-one locally biholomorphic mappings onto the unit disc. Finally, we investigate surjective biholomorphic mappings from Cartesian products of domains.
On multivalent functions of large growth in two directions.
On neighbourhoods of univalent starlike functions
On polynomial expansion of multivalent functions.
On radii of starlikeness and convexity for convolutions of starlike functions.
On Some Correspondence between Holomorphic Functions in the Unit Disc and Holomorphic Functions in the Left Halfplane
We study a correspondence L between some classes of functions holomorphic in the unit disc and functions holomorphic in the left halfplane. This correspondence is such that for every f and w ∈ ℍ, exp(L(f)(w)) = f(expw). In particular, we prove that the famous class S of univalent functions on the unit disc is homeomorphic via L to the class S(ℍ) of all univalent functions g on ℍ for which g(w+2πi) = g(w) + 2πi and .
On some new properties of the spherical curvature of stereographically projected analytic curves.
On some simple sufficient conditions for univalence
In this paper some simple conditions on and which lead to some subclasses of univalent functions will be considered.