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This paper is devoted to the investigation of multidimensional analogues of refined Bohr-type inequalities for bounded holomorphic mappings on the unit polydisc $\mathbb{D}^n$. We establish a sharp extension of the classical Bohr…

Complex Variables · Mathematics 2026-01-13 Molla Basir Ahamed , Sujoy Majumder , Nabadwip Sarkar

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 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…

Complex Variables · Mathematics 2025-12-19 Molla Basir Ahamed , Sujoy Majumder , Nabadwip Sarkar

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

In this article, we determine sharp Bohr-type radii for certain complex integral operators defined on a set of bounded analytic functions in the unit disk.

Complex Variables · Mathematics 2020-08-04 Shankey Kumar , Swadesh Kumar Sahoo

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

The Bohr radius for the class of harmonic functions of the form $ f(z)=h+\overline{g} $ in the unit disk $ \mathbb{D}:=\{z\in\mathbb{C} : |z|<1\} $, where $ h(z)=\sum_{n=0}^{\infty}a_nz^n $ and $ g(z)=\sum_{n=1}^{\infty}b_nz^n $ is to find…

Complex Variables · Mathematics 2022-10-25 Molla Basir Ahamed , Vasudevarao Allu

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

The Bohr radius for a class $\mathcal{G}$ consisting of analytic functions $f(z)=\sum_{n=0}^{\infty}a_nz^n$ in unit disc $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ is the largest $r^*$ such that every function $f$ in the class $\mathcal{G}$…

Complex Variables · Mathematics 2020-07-21 Swati Anand , Naveen Kumar Jain , Sushil Kumar

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…

Complex Variables · Mathematics 2020-09-14 Yong Huang , Ming-Sheng Liu , Saminathan Ponnusamy

We study the $k$-fold symmetric starlike univalent logharmonic mappings of the form $f(z)=zh(z)\overline{g(z)}$ in the unit disk $\mathbb{D}:= \lbrace z \in \mathbb{C}: |z|<1 \rbrace$ with several examples, where $h(z)=\exp…

Complex Variables · Mathematics 2023-08-15 Akash Meher , Priyabrat Gochhayat

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…

Complex Variables · Mathematics 2024-09-17 Shanshan Jia , Ming-Sheng Liu , Saminathan Ponnusamy

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…

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

In this article, we determine the Rogosinski radii for certain subclasses of close-to-convex functions defined on open unit disc $\mathbb{D}= \{z \in \mathbb{C}: |z| < 1\}$. Furthermore, we establish improved versions of the classical Bohr…

Complex Variables · Mathematics 2026-05-25 Shalini Rana , Naveen Kumar Jain

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*}…

Complex Variables · Mathematics 2022-12-13 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

We obtain upper bounds for the norm of the Schwarzian derivative of convex holomorphic mappings defined on the polydisk and the unit ball in $\mathbb{C}^n$. For coordinate-wise convex mappings on the polydisk, we derive a sharp estimate…

Complex Variables · Mathematics 2026-04-15 Rodrigo Hernández

This paper introduces a unified framework for Bohr-type inequalities by incorporating multiple Schwarz functions into the majorant series for $K$-quasiconformal harmonic mappings in the unit disk $\mathbb{D} := \{z\in\mathbb{C} : |z| <…

Complex Variables · Mathematics 2025-10-02 Raju Biswas , Rajib Mandal

Let $ \mathcal{H}(\mathbb{D}) $ be the class of analytic functions in the unit disk $ \mathbb{D} : =\{z\in\mathbb{C} : |z|<1\} $. The classical Bohr's inequality states that if a power series $ f(z)=\sum_{n=0}^{\infty}a_nz^n $ converges in…

Complex Variables · Mathematics 2020-12-14 Molla Basir Ahamed , Vasudevarao Allu , Himadri Halder

The main aim of this paper is to study multidimensional Bohr radii for holomorphic functions defined in complete Reinhardt domains in $\mathbb{C}^n$ with values in complex Banach spaces. More specifically, for holomorphic functions with…

Complex Variables · Mathematics 2026-04-14 Vasudevarao Allu , Himadri Halder , Subhadip Pal
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