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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…

Complex Variables · Mathematics 2022-05-04 Shankey Kumar

In this paper, we first establish a version of multidimensional analogues of the refined Bohr's inequality. Then we establish two versions of multidimensional analogues of improved Bohr's inequality with initial coefficient being zero.…

Complex Variables · Mathematics 2021-03-18 Ming-Sheng Liu , Saminathan Ponnusamy

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,…

Complex Variables · Mathematics 2020-11-05 Stavros Evdoridis , Saminathan Ponnusamy , Antti Rasila

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…

Complex Variables · Mathematics 2026-04-14 Raju Biswas , Rajib Mandal

In this article, we first establish operator-valued analogues of multidimensional refined Bohr inequality. Then we establish operator-valued analogues of multidimensional improved Bohr inequality with a certain power of the norm of the…

Complex Variables · Mathematics 2023-08-29 Sabir Ahammed , Molla Basir Ahamed

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…

Complex Variables · Mathematics 2024-04-30 Shankey Kumar , Saminathan Ponnusamy , G. Brock Williams

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…

Complex Variables · Mathematics 2021-01-12 Bappaditya Bhowmik , Nilanjan Das

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…

Complex Variables · Mathematics 2017-08-21 Ilgiz R Kayumov , Saminathan Ponnusamy

In this paper, we study the Bohr phenomenon for differential operators $D$ and $\mathscr{D}$ of stable harmonic mappings involving multiple Schwarz functions in $\mathcal{B}_n$, using distance formulations. By constructing suitable…

Complex Variables · Mathematics 2025-11-17 Sujoy Majumder , Nabadwip Sarkar , Molla Basir Ahamed

The Bohr radius for an arbitrary class $\mathcal{F}$ of analytic functions of the form $f(z)=\sum_{n=0}^{\infty}a_nz^n$ on the unit disk $\mathbb{D}=\{z\in\mathbb{C} : |z|<1\}$ is the largest radius $R_{\mathcal{F}}$ such that every…

Complex Variables · Mathematics 2024-08-28 Molla Basir Ahamed , Partha Pratim Roy

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…

Functional Analysis · Mathematics 2026-04-15 Vasudevarao Allu , Himadri Halder

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…

Complex Variables · Mathematics 2017-08-21 Ilgiz R Kayumov , Saminathan Ponnusamy

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…

Complex Variables · Mathematics 2025-09-05 Sabir Ahammed , Molla Basir Ahamed , Rajesh Hossain

This article focuses on the Bohr radius problem for the derivatives of analytic functions, along with a technique of establishing Bohr inequalities in classical and generalized settings.

Complex Variables · Mathematics 2019-11-18 Bappaditya Bhowmik , Nilanjan Das

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…

Functional Analysis · Mathematics 2022-01-26 Vern I. Paulsen , Dinesh Singh

A crucial extension of quaternionic function theory to octonions is the concept of slice regular functions, introduced to handle holomorphic-like properties in a non-associative setting. In this paper, first we present a generalization of…

Complex Variables · Mathematics 2025-07-04 Sabir Ahammed , Molla Basir Ahamed

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…

Complex Variables · Mathematics 2025-11-25 Vasudevarao Allu , Raju Biswas , Rajib Mandal

Recently, there has been a number of good deal of research on the Bohr's phenomenon in various setting including a refined formulation of his classical version of the inequality. Among them, in \cite{PaulPopeSingh-02-10} the authors…

Complex Variables · Mathematics 2020-06-12 Saminathan Ponnusamy , Karl-Joachim Wirths

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…

Complex Variables · Mathematics 2024-11-27 Vasudevarao Allu , Raju Biswas , Rajib Mandal

A new counterpart of Schwarz's inequality in inner product spaces and applications for isotonic functionals, integrals and sequences are provided.

Classical Analysis and ODEs · Mathematics 2007-05-23 Sever Silvestru Dragomir