Related papers: Normal harmonic mappings
This paper gives a definition of g-harmonic functions and shows the relation between the g-harmonic functions and g-martingales. It's direct to construct such relation under smooth case, but for continuous case we need the theory of…
In the present paper, we introduced the extended bicomplex plane $\bar{\mathbb{T}}$, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about the convergence of the sequences of…
Estimates are obtained for the initial coefficients of a normalized analytic function $f$ in the unit disk $\mathbb{D}$ such that $f$ and the analytic extension of $f^{-1}$ to $\mathbb{D}$ belong to certain subclasses of univalent…
The aim of this paper is to present a simple way to generate proper monomial rational maps between generalized balls and via the relations between generalized balls and bounded symmetric domains of type I, we suggest new examples of proper…
Brain-mapping techniques have proven to be vital in understanding the molecular, cellular, and functional mechanisms of the brain. Normal anatomical imaging can provide structural information on certain abnormalities in the brain. However…
Via Gauge theory, we give a new proof of partial regularity for harmonic maps in dimension m>2 into arbitrary targets. This proof avoids the use of adapted frames and permits to consider targets of "minimal" C^2 regularity. The proof we…
The main purpose of this note is to provide a topological approach to defining additive functions on Riemannian co-compact normal coverings.
Let $\Delta_k$ be the Dunkl Laplacian on $\mathbb{R}^d$. The main goal of this paper is to characterize $\Delta_k$-harmonic functions by means of a mean value property
In the present paper, we introduce a new subclass of harmonic functions in the unit disc U defined by using the generalized Mittag-Leffler type functions. Coefficient conditions, extreme points, distortion bounds, convex combination are…
The aim of the paper is to give a full characterization of functions f from I into the real line R (where I is an interval in R that satisfies certain natural conditions) such that for any I-valued positive definite kernel K defined on an…
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…
We propose a necessary and sufficient condition for a real-valued function on the real line to be a characteristic function of a probability measures. The statement is given in terms of harmonic functions and completely monotonic functions.
Let $K\ge 1$. We prove Zygmund theorem for $K-$quasiregular harmonic mappings in the unit disk $\mathbb{D}$ in the complex plane by providing a constant $C(K)$ in the inequality $$\|f\|_{1}\le C(K)(1+\|\mathrm{Re}\,(f)\log^+ |\mathrm{Re}\,…
We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk and determine the order of the family of mappings with bounded Schwarzian norm. The result shows that finding the order of the class…
In this article, we determine the radius of univalence of sections of normalized univalent harmonic mappings for which the range is convex (resp. starlike, close-to-convex, convex in one direction). Our result on the radius of univalence of…
In this work we extend the theory of the classical Hardy space $H^1$ to the rational Dunkl setting. Specifically, let $\Delta$ be the Dunkl Laplacian on a Euclidean space $\mathbb{R}^N$. On the half-space $\mathbb{R}_+\times\mathbb{R}^N$,…
Determining the range of complex maps plays a fundamental role in the study of several complex variables and operator theory. In particular, one is often interested in determining when a given holomorphic function is a self-map of the unit…
In this paper, we obtained some normality criteria for families of holomorphic functions. Which generalizes some results of Fang, Xu, Chen and Hua.
We introduce the notion of regular operator mappings of several variables generalising the notion of spectral function. This setting is convenient for studying maps more general than what can be obtained from the functional calculus, and it…
We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of…