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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

In this paper, we first establish the Bohr's theorem for Ces\'aro operator defined for $f\in \mathcal{SRB}(\mathbb{B})$ of slice regular functions in the open unit ball $\mathbb{B}$ of the largest alternative division algebras of octonions…

Complex Variables · Mathematics 2025-12-12 Molla Basir Ahamed , Sabir Ahammed

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

In this paper, we derive the sharp improved versions of Bohr-type inequalities for the Ces\'aro operator acting on the class of bounded analytic functions defined on the unit disk $\D=\left\{z\in\C:\left|z\right|<1\right\}$. In order to…

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

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

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

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 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

In this paper, we first establish an improved Bohr inequality for the class of operator-valued holomorphic functions $f$ on a simply connected domain $\Omega$ in $\mathbb{C}$. Next, we establish a generalization of refined version of the…

Complex Variables · Mathematics 2024-11-07 Sabir Ahammed , Molla Basir Ahamed

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 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

This article introduces the notion of arithmetic Bohr radius for operator valued pluriharmonic functions on complete Reinhardt domains in $\mathbb{C}^n$. Using tools from local Banach space theory, we determine its asymptotic behavior in…

Complex Variables · Mathematics 2026-02-19 Himadri Halder

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…

Complex Variables · Mathematics 2023-03-17 Sabir Ahammed , Molla Basir Ahamed

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.

Complex Variables · Mathematics 2020-06-17 Gang Liu , Zhihong 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 paper, we study Bohr's inequality and refined versions of Bohr-Rogosinski inequalities involving Schwarz functions. Moreover, we establish a version of multidimensional analogue of Bohr inequality and Bohr-Rogosinski inequalities…

Complex Variables · Mathematics 2023-12-12 Sabir Ahammed , Molla Basir Ahamed

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…

Complex Variables · Mathematics 2026-03-18 Vasudevarao Allu , Raju Biswas , Rajib Mandal

In this article, we study Bohr-type inequalities involving a parameter or convex combinations for $K$-quasiconformal, sense-preserving harmonic mappings in $\mathbb{D}$, where the analytic part is subordinate to a convex function. Moreover,…

Complex Variables · Mathematics 2025-09-11 Molla Basir Ahamed , Taimur Rahman

We study generalized Poincar\'e inequalities. We prove that if a function satisfies a suitable inequality of Poincar\'e type, then the Hardy-Littlewood maximal function also obeys a meaningful estimate of similar form. As a by-product, we…

Classical Analysis and ODEs · Mathematics 2021-02-23 Olli Saari

We determine the Bohr radius for the class of odd functions $f$ satisfying $|f(z)|\le 1$ for all $|z|<1$, settling the recent conjecture of Ali, Barnard and Solynin \cite{AliBarSoly}. In fact, we solve this problem in a more general…

Complex Variables · Mathematics 2017-01-17 Ilgiz R Kayumov , Saminathan Ponnusamy