Hölder continuity of conformal mappings and non-quasiconformal Jordan curves.
Holomorphic motions commuting with semigroups
A holomorphic family , |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms , |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions which, in addition, commute with some holomorphic families of holomorphic endomorphisms of , |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.
Hurwitz analysis: basic concepts and connection with Clifford analysis
Hyperbolic and Parabolic Packings.
Hyperbolic and uniform domains in Banach spaces.
Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials
MSC 2010: 30C10, 32A30, 30G35The algebra R(1; j; j2; j3), j4 = ¡1 of the fourth-R numbers, or in other words the algebra of the double-complex numbers C(1; j) and the corresponding functions, were studied in the papers of S. Dimiev and al. (see [1], [2], [3], [4]). The hyperbolic fourth-R numbers form other similar to C(1; j) algebra with zero divisors. In this note the square roots of hyperbolic fourth-R numbers and hyperbolic complex numbers are found. The quadratic equation with hyperbolic fourth-R...
Hyperbolically 1-convex functions
There are two reasonable analogs of Euclidean convexity in hyperbolic geometry on the unit disk 𝔻. One is hyperbolic convexity and the other is hyperbolic 1-convexity. Associated with each type of convexity is the family of univalent holomorphic maps of 𝔻 onto subregions of the unit disk that are hyperbolically convex or hyperbolically 1-convex. The class of hyperbolically convex functions has been the subject of a number of investigations, while the family of hyperbolically 1-convex functions...
Hyperbolically convex functions
We investigate univalent holomorphic functions f defined on the unit disk 𝔻 such that f(𝔻) is a hyperbolically convex subset of 𝔻; there are a number of analogies with the classical theory of (euclidean) convex univalent functions. A subregion Ω of 𝔻 is called hyperbolically convex (relative to hyperbolic geometry on 𝔻) if for all points a,b in Ω the arc of the hyperbolic geodesic in 𝔻 connecting a and b (the arc of the circle joining a and b which is orthogonal to the unit circle) lies in...
Hyperbolically convex functions II
Unlike those for euclidean convex functions, the known characterizations for hyperbolically convex functions usually contain terms that are not holomorphic. This makes hyperbolically convex functions much harder to investigate. We give a geometric proof of a two-variable characterization obtained by Mejia and Pommerenke. This characterization involves a function of two variables which is holomorphic in one of the two variables. Various applications of the two-variable characterization result in...
Images of Disks under Convex and Starlike Functions.
Improved initialization of the accelerated and robust QR-like polynomial root-finding.
Inclusion and neighborhood properties for certain classes of multivalently analytic functions associated with the convolution structure.
Inclusion and neighborhood properties of certain subclasses of analytic, multivalent functions of complex order involving convolution.
Inclusion and neighborhood properties of certain subclasses of analytic and multivalent functions of complex order.
Inclusion and neighborhood properties of certain subclasses of p -valent functions of complex order defined by convolution
In this paper we introduce and investigate three new subclasses of p-valent analytic functions by using the linear operator Dmλ,p(f * g)(z). The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for (n, θ)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.
Inclusion and neighborhood properties of some analytic and multivalent functions.
Inclusion of the roots of a polynomial based on Gerschgorin's theorem.
Inclusion Properties for Certain Classes of Analytic Functions Involving a Family of Fractional Integral Operators
2000 Math. Subject Classification: 30C45A known family of fractional integral operators is used here to define some new subclasses of analytic functions in the open unit disk U. For each of these new function classes, several inclusion relationships are established.
Inclusion properties for certain classes of meromorphic functions associated with a family of linear operators.
Inclusion properties for certain subclasses of analytic functions associated with the Dziok-Srivastava operator.