Related papers: Logarithmic coefficients for certain subclasses of…

We show that for multivariate Freud-type weights $W_\alpha(x)=\exp(-|x|^\alpha)$, $\alpha>1$, any convex function $f$ on $R^d$ satisfying $fW_\alpha\in L_p(R^d)$ if $1\le p<\infty$, or $\lim_{|x|\to\infty}f(x)W_\alpha(x)=0$ if $p=\infty$,…

In this paper, we describe s-logarithmically convex functions in the first and second sense which are connected with the ordinary logatihmic convex and s-convex in the first and second sense. Afterwards, some new inequalities related to…

The Bohr radius for a class $\mathcal{G}$ consisting of analytic functions $f(z)=\sum_{n=0}^{\infty}a_nz^n$ in unit disc $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ is the largest $r^*$ such that every function $f$ in the class $\mathcal{G}$…

For functions $f(z)=z^p+a_{n+1}z^{p+1}+...$ defined on the open unit disk, the condition $\Re (f'(z)/z^{p-1})>0$ is sufficient for close-to-convexity of $f$. By making use of this result, several sufficient conditions for close-to-convexity…

We define the generalized-Euler-constant function $\gamma(z)=\sum_{n=1}^{\infty} z^{n-1} (\frac{1}{n}-\log \frac{n+1}{n})$ when $|z|\leq 1$. Its values include both Euler's constant $\gamma=\gamma(1)$ and the "alternating Euler constant"…

Let $f$ be a holomorphic cusp form of weight $k$ with respect to full modular group $SL_2(\mathbb{Z})$ satisfying a normalized Hecke eigenform, $L_f(s)$ the $L$-function attached to the form $f$. Good gave the approximate functional…

In the present paper, the coefficient estimates are found for the class $\mathcal S^{*-1}(\alpha)$ consisting of inverses of functions in the class of univalent starlike functions of order $\alpha$ in $\mathcal D=\{z\in\mathbb C:|z|<1\}$.…

Let $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ be the class of normalized analytic functions $f$ defined in the domain $|z|<1$ satisfying \begin{align*} {\rm Re\,}…

Let $\mathcal{S}$ denote the class of analytic and univalent ({\it i.e.}, one-to-one) functions $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$. For $f\in \mathcal{S}$, Ma proposed the…

For any natural number $n\in\mathbb{N}$, $ \frac{1}{2n+\frac1{1-\gamma}-2}\le \sum_{i=1}^n\frac1i-\ln n-\gamma<\frac{1}{2n+\frac13}, $ where $\gamma=0.57721566490153286...m$ denotes Euler's constant. The constants $\frac{1}{1-\gamma}-2$ and…

Let $\pi$ be a Hecke-Maass cusp form for $SL(3,\mathbb Z)$ and $f$ be a holomorphic (or Maass) Hecke form for $SL(2,\mathbb{Z})$. In this paper we prove the following subconvex bound $$ L\left(\tfrac{1}{2}+it,\pi\times…

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

In this paper, we investigate the sharp bounds of the second Hankel determinant of Logarithmic coefficients for the starlike and convex functions with respect to symmetric points in the open unit disk.

Let $\mathcal{V}_p(\lambda)$ be the collection of all functions $f$ defined in the unit disc $\ID$ having a simple pole at $z=p$ where $0<p<1$ and analytic in $\ID\setminus\{p\}$ with $f(0)=0=f'(0)-1$ and satisfying the differential…

We consider the family of all meromorphic functions $f$ of the form $$ f(z)=\frac{1}{z}+b_0+b_1z+b_2z^2+\cdots $$ analytic and locally univalent in the puncture disk $\mathbb{D}_0:=\{z\in\mathbb{C}:\,0<|z|<1\}$. Our first objective in this…

There are many results for sufficient conditions of functions f(z) which are analytic in the open unit disc U to be starlike and convex in U. The object of the present paper is to derive some interesting sufficient conditions for f(z) to be…

We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of $2\pi$-periodic functions, which are represented by convolutions of functions $\varphi (\varphi\bot 1)$ from unit ball of…

In this paper we study the class $\mathcal{U}$ of functions that are analytic in the open unit disk ${\mathbb D}=\{z:|z|<1\}$, normalized such that $f(0)=f'(0)-1=0$ and satisfy \[\left|\left [\frac{z}{f(z)} \right]^{2}f'(z)-1…

We consider the Lommel functions $s_{\mu,\nu}(z)$ for different values of the parameters $(\mu,\nu)$. We show that if $(\mu,\nu)$ are half integers, then it is possible to describe these functions with an explicit combination of polynomials…

We study the convolution of functions of the form \[ f_\alpha (z) := \dfrac{\left( \frac{1 + z}{1 - z} \right)^\alpha - 1}{2 \alpha}, \] which map the open unit disk of the complex plane onto polygons of 2 edges when $\alpha\in(0,1)$. We…