Related papers: A note on the Bohr inequality

In this article several types of inequalities for weighted sums of the moduli of Taylor coefficients for Bloch functions are proved

We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…

We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration…

Higher order Bernstein- and Markov-type inequalities are established for trigonometric polynomials on compact subsets of the real line and algebraic polynomials on compact subsets of the unit circle. In the case of Markov-type inequalities…

In a recent paper, Ramos and Tilli proved certain sharp inequality for analytic functions in subdomains of the unit disk. We will generalize their main inequality for derivatives of functions from Bergman space with respect to two diferent…

We revisit Hardy's inequality in the scope of regular Dirichlet forms following an analytical method. We shall give an alternative necessary and sufficient condition for the occurrence of Hardy's inequality. A special emphasis will be given…

A generalization of Mercer inequality for h-convex function is presented. As application, a weighted generalization of triangle inequality is given.

In this paper our aim is to find the radii of starlikeness and convexity of the normalized Wright functions for three different kind of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for…

Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…

Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.

In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.

This article implements a simple convex approach and block techniques to obtain several new refined versions of numerical radius inequalities for Hilbert space operators. This includes comparisons among the norms of the operators, their…

Boggio's formula in balls is known for integer-polyharmonic Dirichlet problems and for fractional Dirichlet problems with fractional parameter less than 1. We give here a consistent formulation for fractional polyharmonic Dirichlet problems…

The present article concerns the Bohr radius for $K$-quasiconformal sense-preserving harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ for which the analytic part $h$ is subordinated to some analytic function $\varphi$, and…

Let $H^{\infty}(\Omega,X)$ be the space of bounded analytic functions $f(z)=\sum_{n=0}^{\infty} x_{n}z^{n}$ from a proper simply connected domain $\Omega$ containing the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ into a complex…

In this paper we shall study the inverse problem relative to dynamics of the w function which is a special arithmetic function and shall get some results.

Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…

Let $\mathcal{H}$ be the class of normalized complex valued harmonic functions $ f = h + \overline{g}$ defined on the unit disk $\mathbb{D}$, where $h$ and $g$ are analytic functions with the normalization conditions $h(0) = h'(0) - 1 = 0$…

In this paper we point out that the commonly used error bound in the theory of radial basis functions contains an important error. It doesn't apply for derivatives. Thus one should be very careful when dealing with differential equations.

We establish an operator extension of the following generalization of Bohr's inequality, due to M.P. Vasi\'c and D.J. Ke\v{c}ki\'{c}: $$|\sum_{i=1}^n z_i|^r \leq (\sum_{i=1}^n \alpha_i^{1/(1-r)})^{r-1}\sum_{i=1}^n \alpha_i|z_i|^r \quad…