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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…

Complex Variables · Mathematics 2019-05-27 ZhiHong Liu , Saminathan Ponnusamy

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

Complex Variables · Mathematics 2020-12-15 Molla Basir Ahamed , Vasudevarao Allu , Himadri Halder

This paper is devoted to the investigation of multidimensional analogues of refined Bohr-type inequalities for bounded holomorphic mappings on the unit polydisc $\mathbb{P}\Delta(0;1_n)$. We provide a definitive resolution to the Bohr…

Complex Variables · Mathematics 2026-03-05 Molla Basir Ahamed , Sujoy Majumder , Debabrata Pramanik

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…

Complex Variables · Mathematics 2021-04-23 Yong Huang , Ming-Sheng Liu , Saminathan Ponnusamy

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…

Complex Variables · Mathematics 2019-04-01 Seraj A. Alkhaleefah , Ilgiz R Kayumov , Saminathan Ponnusamy

In this paper, we first determine Bohr's inequality for the class of harmonic mappings $f=h+\overline{g}$ in the unit disk $\ID$, where either both $h(z)=\sum_{n=0}^{\infty}a_{pn+m}z^{pn+m}$ and $g(z)=\sum_{n=0}^{\infty}b_{pn+m}z^{pn+m}$…

Complex Variables · Mathematics 2021-03-18 Yong Huang , Ming-Sheng Liu , 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

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…

Complex Variables · Mathematics 2026-04-01 Molla Basir Ahamed , Sanju Mandal

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

We consider the class of \emph{stable} harmonic mappings $f=h+\overline{g}$ introduced by Martin, Hernandez, and the class of \emph{stable} logharmonic mappings $f=zh\overline{g}$ introduced by AbdulHadi, El-Hajj. We determine Bohr's radius…

Complex Variables · Mathematics 2022-03-25 Zayid Abdulhadi , Layan El Hajj

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

Let $K(B_{\ell_p^n},B_{\ell_q^n}) $ be the $n$-dimensional $(p,q)$-Bohr radius for holomorphic functions on $\mathbb C^n$. That is, $K(B_{\ell_p^n},B_{\ell_q^n}) $ denotes the greatest constant $r\geq 0$ such that for every entire function…

Complex Variables · Mathematics 2017-12-22 Daniel Galicer , Martín Mansilla , Santiago Muro

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…

Complex Variables · Mathematics 2017-09-27 Stavros Evdoridis , Saminathan Ponnusamy , Antti Rasila

The classical Bohr theorem and its subsequent generalizations have become active areas of research, with investigations conducted in numerous function spaces. Let $\{\psi_n(r)\}_{n=0}^\infty$ be a sequence of non-negative continuous…

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

We study the asymptotic decay of the Fourier spectrum of real functions $f\colon \{-1,1\}^N \rightarrow \mathbb{R}$ in the spirit of Bohr's phenomenon from complex analysis. Every such function admits a canonical representation through its…

Functional Analysis · Mathematics 2017-07-31 Andreas Defant , Mieczysław Mastyło , Antonio Pérez

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…

Complex Variables · Mathematics 2025-09-26 Adesanmi Mogbademu , Ismaila Amusa

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

Let $\mathcal{H}$ be the space of all functions that are analytic in $\mathbb{D}$. Let $\mathcal{A}$ denote the family of all functions $f\in\mathcal{H}$ and normalized by the conditions $f(0)=0=f'(0)-1$. Obradovi\'{c} and Ponnusamy have…

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

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…

Complex Variables · Mathematics 2023-02-16 Kaixin Chen , Ming-Sheng Liu , Saminathan Ponnusamy

In this article, we first establish a generalized Bohr inequality and examine its sharpness for a class of analytic functions $f$ in a simply connected domain $\Omega_\gamma,$ where $0\leq \gamma<1$ with a sequence $\{\varphi_n(r)…

Complex Variables · Mathematics 2024-05-06 Sabir Ahammed , Molla Basir Ahamed , Partha Pratim Roy