Related papers: Sufficiency for Nephroid Starlikeness using Hyperg…

In this paper we introduce some new methods to understand the analytic behaviour of the zeta function of a group. We can then combine this knowledge with suitable Tauberian theorems to deduce results about the growth of subgroups in a…

For $\alpha\geq 0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}_{\beta}(\alpha,\gamma)$ satisfies the condition \begin{align*} {\rm Re\,} \left( e^{i\phi}\left((1-\alpha+2\gamma)f/z+(\alpha-2\gamma)f'+ \gamma…

In this paper, we introduce a family of analytic functions given by $$\psi_{A,B}(z):= \dfrac{1}{A-B}\log{\dfrac{1+Az}{1+Bz}},$$ which maps univalently the unit disk onto either elliptical or strip domains, where either $A=-B=\alpha$ or…

Ma-Minda class (of starlike functions) consists of all normalized analytic functions $f$ on the unit disk for which the image of $zf'(z)/f(z)$ is contained in the some starlike region in the right-half plane. We obtain the best possible…

Let $h$ and $g$ be two analytic functions in the unit disc $\Delta$ that $g(0)=1$. Also let $\beta$ be a complex number with ${\rm Re}\{\beta\}>-1/2$. A function $f$ is said to be log--harmonic mapping if it has the following representation…

Let ${\mathcal M}$ be the class of analytic functions in the unit disk $\ID$ with the normalization $f(0)=f'(0)-1=0$, and satisfying the condition $$\left |z^2\left (\frac{z}{f(z)}\right )''+ f'(z)\left(\frac{z}{f(z)} \right)^{2}-1\right…

For $0\leq \alpha <1$, the sharp radii of starlikeness and convexity of order $\alpha$ for functions of the form $f(z)=z+a_2z^2+a_3z^3+...$ whose Taylor coefficients $a_n$ satisfy the conditions $|a_2|=2b$, $0\leq b\leq 1$, and $|a_n|\leq n…

For $-1\le B<A\le 1$, let $\mathcal{S}^*(A,B)$ denote the class of normalized analytic functions $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ in $|z|<1$ which satisfy the subordination relation $zf'(z)/f(z)\prec (1+Az)/(1+Bz)$ and $\Sigma^*(A,B)$…

Let $F$ be a $p$-adic field and let $G$ be a connected reductive group defined over $F$. We assume $p$ is big. Denote $\mathfrak{g}$ the Lie algebra of $G$. To each vertex $s$ of the reduced Bruhat-Tits' building of $G$, we associate as…

In this work we consider a family of function classes constructed by means of the Gauss hypergeometric function $_2F_1(1,1;2;z) =-\frac{\log(1-z)}{z}$. We demonstrate that this family, in fact, constitutes classes of analytic functions…

For a normalised analytic function f defined on the open unit disk in the complex plane, we determine several sufficient conditions for starlikeness in terms of the quotients Q_{ST}:=zf'(z)/f(z), Q_{CV}:=1+zf"(z)/f'(z) and the Schwarzian…

We investigate the non-univalent function's properties reminiscent of the theory of univalent starlike functions. Let the analytic function $\psi(z)=\sum_{i=1}^{\infty}A_i z^i$, $A_1\neq0$ be univalent in the unit disk. Non-univalent…

For the standard Ma-Minda class $\mathcal{S}^{*}(\psi)$ of univalent starlike functions, we derive $\mathcal{S}^{*}(\psi)$-radii for some well-known special functions. In addition, we obtain the set of extremal functions for the classical…

In the present investigation, we introduce a new subclass of starlike functions defined by $\mathcal{S}^{*}_{\tau}:=\{f\in \mathcal{A}:zf'(z)/f(z) \prec 1+\arctan z=:\tau(z)\}$, where $\tau(z)$ maps the unit disk $\mathbb {D}:= \{z\in…

Let $\mathcal{H}$ be the space of all functions that are analytic in $\mathbb{D}$. Let $\mathcal{A}$ denote the family of all functions $f\in\mathcal{H}$ and normalized by the conditions $f(0)=0=f'(0)-1$. Obradovi\'{c} and Ponnusamy have…

Assume that $\Delta$ is the open unit disk in the complex plane and $\mathcal{A}$ is the class of normalized analytic functions in $\Delta$. In this paper we introduce and study the class \begin{equation*} \mathcal{BS}(\alpha):=\left\{f\in…

Let $\mathcal{A}$ denote the set of all analytic functions $f$ in the unit disk $\ID=\{z:\,|z|<1\}$ of the form $f(z)=z+\sum_{n=2}^{\infty}a_nz^n.$ Let $\mathcal{U}$ denote the set of all $f\in \mathcal{A}$, $f(z)/z\neq 0$ and satisfying…

In this paper, we introduce and investigate a novel subclass $\Sigma(\theta, \lambda, \gamma)$ of meromorphic functions defined in the punctured unit disk ${D}^*$. This class is constructed utilizing a specialized generalized operator…

Let $\mathcal{A}$ be the family of functions $f(z)=z+a_2z^2+...$ which are analytic in the open unit disc $\mathbb{D}=\{z: |z|<1 \}$, and denote by $\pe$ of functions $p(z)=z+p_1z+p_2z^2+...$ analytic in $\de$ such that $p(z)$ is in $\pe$…

Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little…