Related papers: On certain subclasses of analytic and harmonic map…

We give some coefficient bounds and distortion theorems for a subclass of univalent functions in the unit disk, and defined using the S\^{a}l\^{a}gean differential operator. The results generalize and unify some well known results for…

In this paper, we investigate properties of harmonic entire mappings. Firstly, we give the characterizations of the order and the type for a harmonic entire mapping $f=h+\overline{g}$, respectively, and also consider the relationship…

In this paper, we consider a general subclass of analytic and bi-univalent functions in the open unit disk in the complex plane. Making use of the Chebyshev polynomials, we obtain upper bound estimate for the second Hankel determinant for…

In 2011, Sok\'{o}{\l} (Comput. Math. Appl. 62, 611--619) introduced and studied the class $\mathcal{SK}(\alpha)$ as a certain subclass of starlike functions, consists of all functions $f$ ($f(0)=0=f'(0)-1$) which satisfy in the following…

The sharp bound for the third Hankel determinant for the coefficients of the inverse function of starlike function of order $1/2$ is obtained. In light of this, we can deduce that the functionals $|H_3(1)(f)|$ and $|H_3(1)(f^{-1})|$ exhibit…

Let $p$ be an analytic function defined on the open unit disc $\mathbb{D}$ with $p(0)=1$ and $0< \alpha \leq 1$. The conditions on complex valued functions $C$, $D$ and $E$ are obtained for $p$ to be subordinate to $((1+z)/(1-z))^{\alpha}$…

For the error functions of the form \begin{equation*} E_{r}\mathfrak{f}(z)=\frac{\sqrt{\pi z}}{2}er\ \mathfrak{f}(\sqrt{z})=z+\Sigma_{n=2}^{\infty} \frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}, \end{equation*}% let…

Let $\mathcal{S}$ denote the class of functions $f$ which are analytic and univalent in the unit disk ${\mathbb D}=\{z:|z|<1\}$ and normalized with $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. Using a method based on Grusky coefficients we study…

In this paper, we define certain subclass of harmonic univalent function in the unit disc U = {z in C :|z|<1} by using q-differential operator. Also we obtain coefficient inequalities, growth and distortion theorems for this subclass.

Let $\ast$ and $\widetilde {\ast}$ denote the convolution of two analytic maps and that of an analytic map and a harmonic map respectively. Pokhrel [1] proved that if $f = h+\overline{g}$ is a harmonic map convex in the direction of…

A class of subharmonic functions represented by the modified kernels are proved to have the growth estimates $u(z)= o(y^{1-\alpha}|z|^{m+\alpha})$ at infinity in the upper half plane ${\bf C}_{+}$, which generalizes the growth properties of…

Planar functions are of great importance in the constructions of DES-like iterated ciphers, error-correcting codes, signal sets and the area of mathematics. They are defined over finite fields of odd characteristic originally and…

Let $f$ be a holomorphic function on the strip $\{z\in C: -\alpha<Im z<\alpha\}, \alpha > 0$, belonging to the class $H(\alpha,-\alpha;\epsilon)$ defined below. It is shown that there exist holomorphic functions $w_1$ on $\{z\in C: 0<Im z…

Analytic functions in the Hardy class $H^2$ over the upper half-plane $\mathbb{H}_+$ are uniquely determined by their values on any curve $\Gamma$ lying in the interior or on the boundary of $\mathbb{H}_+$. The goal of this paper is to…

We establish a necessary and sufficient condition on a continuous function on $[-1,1]$ under which the family of functions on the unit sphere $\mathbb{S}^{d-1}$ constructed in the described manner is fundamental in $C(\mathbb{S}^{d-1})$. In…

We prove a contraction property of certain classes of smooth functions, whose absolute values of elements are log-hyperharmonic functions in the unit ball, thus extending the results of Kulikov to higher-dimensional space (GAFA (2022)).…

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent…

This paper studies analytic functions $f$ defined on the open unit disk of the complex plane for which $f/g$ and $(1+z)g/z$ are both functions with positive real part for some analytic function $g$. We determine radius constants of these…

Let $\mathcal{A}$ denote the class of analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ normalized by $f(0)=0$, $f'(0)=1$. For $-\pi/2<\alpha<\pi/2$, let $\mathcal{S}_{\alpha}$ be the subclass of $\mathcal{A}$…

For $\lambda\ge0$, a $C^2$ function $f$ defined on the unit disk ${{\mathbb D}}$ is said to be $\lambda$-analytic if $D_{\bar{z}}f=0$, where $D_{\bar{z}}$ is the (complex) Dunkl operator given by…