Related papers: On functions starlike with respect to $n$-ply symm…

Let $z$ be the activity of point particles described by classical equilibrium statistical mechanics in ${\bf R}^\nu$. The correlation functions $\rho^z(x_1,\dots,x_k)$ denote the probability densities of finding $k$ particles at…

\noindent In the present investigation, we find the sharp bound of fifth coefficient of analytic normalized function $f$ satisfying $z f'(z)/f(z) \prec \varphi(z)$ when coefficients of $\varphi$ satisfy certain conditions. For an…

Recent advances in image and signal processing have drawn on geometric function theory, particularly coefficient estimate problems. Motivated by their significance, we introduce a class of starlike functions related to a balloon-shaped…

In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disk. We also estimate the coefficient bound and obtain growth, covering and area theorems for…

Let $\mathcal{P}$ denote the Carath\'{e}odory class accommodating all the analytic functions $p$ having positive real part and satisfying $p(0)=1$. In this paper, the second coefficient of the normalized analytic function $f$ defined on the…

Brannan showed that a normalized univalent polynomial of the form $P(z)=z+a_2 z^2+\ldots + a_{n-1}z^{n-1}+\frac{z^n}{n}$ is starlike if and only if $a_2=\ldots=a_{n-1}=0$. We give a new and simple proof of his result, showing further that…

In this paper, we study analytic and geometric properties of the solution $q(z)$ to the differential equation $q(z)+zq'(z)/q(z)=h(z)$ with the initial condition $q(0)=1$ for a given analytic function $h(z)$ on the unit disk $|z|<1$ in the…

Sufficient conditions are obtained on the parameters of Lommel function of the first kind, generalized Struve function of the first kind and the confluent hypergeometric function under which these special functions become exponential convex…

We consider a $G$-function $F(z)=\sum_{k=0}^{\infty} A_k z^k \in \mathbb{K}[[z]]$, where $\mathbb{K}$ is a number field, of radius of convergence $R$ and annihilated by the $G$-operator $L \in \mathbb{K}(z)[\mathrm{d}/\mathrm{d}z]$, and a…

Let $\mathcal{S}^*(\varphi)$ be the class of all analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$, normalized by $f(0)=f'(0)-1=0$ that satisfy the subordination relation $zf'(z)/f(z)\prec\varphi(z)$, where…

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…

Let $E$ be an arbitrary closed set on the unit circle $\partial \mathbb{D}$, u be a harmonic function on the unit disk $\mathbb{D}$ satisfying $|u(z)|\lesssim (1-|z|)^\gamma \rho^{-q}(z)$ where $\rho(z)= \mathop{\rm dist}(z, E)$, $\gamma$,…

Let $\mathcal{A}$ be the set of all analytic functions $f$ defined in the open unit disk $\mathbb{D}$ and satisfying $f(0)=f'(0)-1=0$. In this paper, we consider the function $\varphi_{\scriptscriptstyle {Ne}}(z):=1+z-z^3/3$, which maps the…

We establish for $2 \le k \le n-1$ the strict concavity of the function $f_k(\lambda)=\log(\sigma_k(\lambda))$ on a subset of the positive cone $\Gamma_n=\{\lambda=(\lambda_{1}, \lambda_{2}, \cdots,\lambda_{n})\in \mathbb{R}^n;…

This article is devoted to the study of several algebras which are related to symmetric functions, and which admit linear bases labelled by various combinatorial objects: permutations (free quasi-symmetric functions), standard Young…

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…

For an analytic and univalent function $f$ in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f'(0)-1$, the logarithmic coefficients $\gamma_n$ are defined by $\log \frac{f(z)}{z}= 2\sum_{n=1}^{\infty}…

The main objective of the present article is to make interconnection between the Generalized Hyergeometric series and some subclasses of normalized analytic functions with positive(Tailor's) coefficients in the open unit disc $\mathbb{D}…

In this study, we deal with the sharp bounds of certain Toeplitz determinants whose entries are the logarithmic coefficients of analytic univalent functions $f$ such that the quantity $z f'(z)/f(z)$ takes values in a specific domain lying…

In this paper we define a new concept of quasi-convolution for analytic functions normalized by $f(0)=0$ and $f^\prime(0)=1$ in the unit disk $E=\{z\in \mathbb{C}\colon |z|<1\}$. We apply this new approach to study the closure properties of…