Related papers: Harmonic spirallike functions and harmonic strongl…
This research aimed to introduce the concept of harmonically m-concave set-valued functions, which is obtained from the combination of two definitions: harmonically m-concave functions and set-valued functions. In this work some properties…
Matrix elements of spinor and principal series representations of the Lorentz group are studied in the basis of complex angular momentum (helicity basis). It is shown that matrix elements are expressed via hyperspherical functions…
We consider the class $\mathcal{S}^*(q_c)$ of normalized starlike functions $f$ analytic in the open unit disk $|z|<1$ that satisfying the inequality \begin{equation*} \left|\left(\frac{zf'(z)}{f(z)}\right)^2-1\right|<c \quad (0<c\leq1).…
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…
In this paper we study the boundary values of harmonic and holo- morphic functions in the weighted Hardy spaces on the unit disk $\mathbb{D}$. These spaces were introduced by Poletsky and Stessin in [6] for plurisubharmonic functions on…
n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…
Monogenic functions are basic to Clifford analysis. On Euclidean space they are defined as smooth functions with values in the corresponding Clifford algebra satisfying a certain system of first order differential equations, usually…
We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and the other one is a generalized Mathieu type power series involving factorials in its coefficients.…
In this paper, we consider the generating functions of the complete and elementary symmetric functions and provide a new generalization of these classical symmetric functions. Some classical relationships involving the complete and…
Let a function $u(x,y)$ be harmonic in the domain $$ D\times V_r=D\times \{y\in \mathbb{R}^m: |y|<r\}\subset \mathbb{R}^n\times \mathbb{R}^m $$ and for each fixed point $x^0$ from some a set $E\subset D$, %which is not embedded in countable…
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…
The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes SP_{p}({\alpha},\b{eta}) and UCV_{p}({\alpha},\b{eta}) of uniformly spirallike functions.…
We study the class $HQ(\mathbb{D})$, the set of harmonic quasiconformal automorphisms of the unit disk $\mathbb{D}$ in the complex plane, endowed with the topology of uniform convergence. Several important topological properties of this…
Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes…
For every $q\in(0,1)$ and $0\le \alpha<1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $\alpha$, on the open unit disk. We study this class of functions and explore some inclusion properties with…
In this paper, we introduce and explore a new class of starlike functions denoted by $\mathcal{S}^*_{\mathfrak{B}}$, defined as follows: $$\mathcal{S}^*_{\mathfrak{B}}=\{f\in \mathcal{A}:zf'(z)/f(z)\prec…
The primary objective of this work is to obtain some sufficient conditions so that normalized Gauss hypergeometric function satisfies exponential starlikeness and convexity in the unit disk. Moreover, conditions on parameter of this…
We analyze the structural and dynamical properties of disk-like objects formed in fully consistent cosmological simulations which include inefficient star formation. Comparison with data of similar observable properties of spiral galaxies…
Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent properties, making…
We establish sharp $L^p$ integral mean estimates for $(\alpha,\beta)$-harmonic functions on the unit disk. Explicit bounds for the functions and their partial derivatives are obtained in terms of boundary data, by means of the associated…