Related papers: Refined Bohr inequality for functions in $\mathbb{…
In this paper, we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball $B_X$ of a complex Banach space $X$ into $\mathbb{C}$. As applications, we will establish refined Bohr…
In this paper, we investigates the Bohr phenomenon for holomorphic mappings $F$ from the unit ball $\mathbb{B}_X$ of a complex Banach space $X$ into the closure of the unit polydisc $\mathbb{D}^m$ within the space $\mathbb{C}^m$. First, we…
Our first aim of this article is to establish several new versions of refined Bohr inequalities for bounded analytic functions in the unit disk involving Schwarz functions. Secondly, %as applications of these results, we obtain several new…
Based on improving the classical Bohr inequality, we get in this paper some refined versions for a quasi-subordination family of functions, one of which is key to build our results. By means of these investigations, for a family of harmonic…
In this paper, we study the Bohr inequality with lacunary series for vector-valued holomorphic functions defined in unit ball of finite dimensional Banach sequence space. Also, we study the Bohr-Rogosinski inequality for same class of…
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.
The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{D}^n$.We also prove two other sharp versions of the Bohr inequality in the setting…
In this paper, we study the Bohr phenomenon for functions that are defined on a general simply connected domain of the complex plane. We improve known results of R. Fournier and St. Ruscheweyh for a class of analytic functions. Furthermore,…
In this paper, we study the Bohr inequality with lacunary series to the single valued (resp. vector-valued) holomorphic function defined in unit ball of finite dimensional Banach sequence space. Also, we extend the Bohr inequality with an…
In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.
The primary objective of this paper is to establish several sharp results concerning the Bohr inequality, the refined Bohr inequality, and the improved Bohr inequality for the classes of analytic functions and harmonic mappings defined on…
The primary objective of this paper is to establish several sharp versions of improved Bohr inequalities, refined Bohr inequalities, and Bohr-Rogosinski inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings…
In this paper, we study some improved and refined versions of the classical Bohr inequality applicable to the class $\mathcal{B}$, which consists of self-analytic mappings defined on the unit disk $\mathbb{D}$. First, we improve the Bohr…
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…
In this article, Bohr type inequalities for some complex valued harmonic functions defined on the unit disk are given. All the results are sharp.
In this paper, a significant improvement has been achieved in the classical Bohr's inequality for the class $ \mathcal{B} $ of analytic self maps defined on the unit disk $ \mathbb{D} $. More precisely, we generalize and improve several…
The primary objective of this paper is to establish several sharp versions of improved Bohr inequality, refined Bohr-type inequality, and refined Bohr-Rogosinski inequality for the class of $K$-quasiconformal sense-preserving harmonic…
In this paper, we establish five new sharp versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing Schwarz function in place of the initial coefficients in the power series representations of the…
We prove several improved versions of Bohr's inequality for the harmonic mappings of the form $f=h+\overline{g}$, where $h$ is bounded by 1 and $|g'(z)|\le|h'(z)|$. The improvements are obtained along the lines of an earlier work of Kayumov…
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 $h(0) = h'(0) - 1 = 0$…