Related papers: Improved Bohr's phenomenon in quasi-subordination …

This article investigates the Bohr phenomenon and sharp coefficient problems for the class $\mathcal{A}_{\beta}$, a subclass of analytic self-maps of the unit disk with the holomorphic generators of one-parameter continuous semigroups. By…

We determine the Bohr radius for the class of all functions $f$ of the form $f(z)=\sum_{k=1}^\infty a_{kp+m} z^{kp+m}$ analytic in the unit disk $|z|<1$ and satisfy the condition $|f(z)|\le 1$ for all $|z|<1$. In particular, our result also…

In this paper, we first establish an improved Bohr inequality for the class of operator-valued holomorphic functions $f$ on a simply connected domain $\Omega$ in $\mathbb{C}$. Next, we establish a generalization of refined version of the…

We present a new elementary proof of a theorem due to Harald Bohr, which states that an unbounded, analytic, and almost periodic function in a half-plane can be written as the sum of two analytic functions: the first is unbounded and…

Let $ \mathcal{H}(\Omega) $ be the class of complex-valued functions harmonic in $ \Omega\subset\mathbb{C} $ and each $f=h+\overline{g}\in \mathcal{H}(\Omega)$, where $ h $ and $ g $ are analytic. In the study of Bohr phenomenon for certain…

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…

Wiegerinck has shown that a separately subharmonic function need not be subharmonic. Improving previous results of Lelong, of Avanissian, of Arsove and of us, Armitage and Gardiner gave an almost sharp integrability condition which ensures…

A class $ \mathcal{F} $ consisting of analytic functions $ f(z)=\sum_{n=0}^{\infty}a_nz^n $ in the unit disc $ \mathbb{D}=\{z\in\mathbb{C}:|z|<1\} $ satisfies a Bohr phenomenon if there exists an $ r_f>0 $ such that \begin{equation*}…

The classical inequality of Bohr concerning Taylor coeficients of bounded holomorphic functions on the unit disk, has proved to be of significance in answering in the negative the conjecture that if the non-unital von Neumann inequality…

For $f(z) = \sum_{n=0}^{\infty} a_n z^n$ and a fixed $z$ in the unit disk, $|z| = r,$ the Bohr operator $\mathcal{M}_r$ is given by \[\mathcal{M}_r (f) = \sum_{n=0}^{\infty} |a_n| |z^n| = \sum_{n=0}^{\infty} |a_n| r^n.\] This papers…

The aim of this paper is to introduce and to study an algebra of almost periodic generalized functions containing the classical Bohr almost periodic functions as well as almost periodic Schwartz distributions

Let $ \mathcal{H} $ be the class of complex-valued harmonic mappings $ f=h+\bar{g}$ defined in the unit disk $ \mathbb{D} : =\{z\in\mathbb{C} : |z|<1\} $, where $ h $ and $ g $ are analytic functions in $ \mathbb{D} $ with the normalization…

The main aim of this paper is to prove a generalization of the classical Bohr theorem and as an application, we obtain a counterpart of Bohr theorem for the generalized Ces\'aro operator.

In this paper we establish a refinement of the companion of Ostrowski inequality for functions of bounded variation. Applications for the trapezoid inequality, the mid-point inequality, and to probability density functions are also given.

There are a number of articles which deal with Bohr's phenomenon whereas only a few papers appeared in the literature on Rogosinski's radii for analytic functions defined on the unit disk $|z|<1$. In this article, we introduce and…

In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further,…

We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…

This paper mainly uses the nonnegative continuous function $\{\zeta_n(r)\}_{n=0}^{\infty}$ to redefine the Bohr radius for the class of analytic functions satisfying $\real f(z)<1$ in the unit disk $|z|<1$ and redefine the Bohr radius of…

First, we give the definition for quasi-nearly subharmonic functions, now for general, not necessarily nonnegative functions, unlike previously. We point out that our function class incudes, among others, quasisubharmonic functions, nearly…

In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)