Related papers: A Simple Proof of Bohr's Inequality
Operator-valued multivariable Bohr type inequalities are obtained for: a class of noncommutative holomorphic functions, generalizing the analytic functions on the open unit disc; the noncommutative disc algebra and the noncommutative…
In this article we establish Bohr inequalities for operator valued functions, which can be viewed as the analogues of a couple of interesting results from scalar valued settings. Some results of this paper are motivated by the classical…
In this paper, firstly we prove two refined Bohr-type inequalities associated with area for bounded analytic functions $f(z)=\sum_{n=0}^{\infty}a_{n}z^{n}$ in the unit disk. Later, we establish the Bohr-type operator on analytic functions…
This article is devoted to the sharp improvement of the classical Bohr inequality for bounded analytic functions defined on the unit disk. We also prove two other sharp versions of the Bohr inequality by replacing the constant term by the…
Let $\mathcal{B}(\mathcal{H})$ denote the Banach algebra of all bounded linear operators acting on complex Hilbert spaces $\mathcal{H}$. In this paper, we first establish several sharply refined versions of Bohr's inequality analogues with…
The purpose of this article is to study Bohr inequalities involving the absolute values of the coefficients of an operator valued function. To be more specific, we establish an operator valued analogue of a classical result regarding the…
The primary objective of this paper is to establish several sharp versions of Bohr inequalities for bounded analytic functions in the unit disk $\mathbb{D} := \{z\in\mathbb{C} : |z| < 1\}$ involving multiple Schwarz functions. Moreover, we…
In this article, some Bohr inequalities for analytical functions on the unit disk are generalized to the forms with two parameters. One of our results is sharp.
We study Bohr type inequalities within the framework of fractional calculus. Using Riemann Liouville fractional differential and integral operators, we establish generalized Bohr radii for analytic functions in the unit disk, including the…
In this article, by combining appropriate refined Bohr's inequalities with some techniques concerning bounded analytic functions defined in the unit disk, we generalize and improve several Bohr type inequalities for such functions.
In this paper, we introduce the study of the Bohr phenomenon for a quasi-subordination family of functions, and establish the classical Bohr's inequality for the class of quasisubordinate functions. As a consequence, we improve and obtain…
Bohr's classical theorem and its generalizations are now active areas of research and have been the source of investigations in numerous function spaces. In this article, we study a generalized Bohr's inequality for the class of bounded…
The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{P}\Delta(0;1_n)$. We also prove two other sharp versions of the Bohr inequality in…
Multivariable operator theory is used to provide Bohr inequalities for free holomorphic functions with operator coefficients on the regular polyball. In addition, we obtain analogues of Caratheodory, Fejer, and Egervary-Szazs inequalities…
In this article, we study the Bohr type inequality for {C}es\'{a}ro operator and {B}ernardi integral operator acting on the space of analytic functions defined on a simply connected domain containing the unit disk $\mathbb{D}$.
In this paper, we first obtain a refined version of the Bohr inequality of norm-type for holomorphic mappings with lacunary series on the polydisk in $\mathbb{C}^n$ under some restricted conditions. Next, we determine the refined version of…
Let $\mathcal{B}(\mathcal{H})$ be the algebra of all bounded linear operators on a complex Hilbert space $\mathcal{H}$. In this paper, we first establish several sharp improved and refined versions of the Bohr's inequality for the functions…
In this paper, we establish several new versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing $\varphi=\{\varphi_n(r)\}^{\infty}_{n=0}$ in place of the $\{r^n\}^{\infty}_{n=0}$ in the power series…
In this article, Bohr type inequalities for some complex valued harmonic functions defined on the unit disk are given. All the results are sharp.
Slice regular functions are a generalization of holomorphic functions to the setting of quaternions (and more generally, Clifford algebras). In this paper, we first establish the Bohr inequality for slice starlike functions and slice…