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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

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 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 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

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

This article is devoted to the sharp improvement of the classical Bohr inequality for bounded analytic functions defined on the unit disk. We also prove two other sharp versions of the Bohr inequality by replacing the constant term by the…

Complex Variables · Mathematics 2020-04-21 Amir Ismagilov , Ilgiz R Kayumov , Saminathan Ponnusamy

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

In this article, some Bohr inequalities for analytical functions on the unit disk are generalized to the forms with two parameters. One of our results is sharp.

Complex Variables · Mathematics 2025-08-12 Jianying Zhou , Qihan Wang , Boyong Long

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

In this paper we first consider another version of the Rogosinski inequality for analytic functions $f(z)=\sum_{n=0}^\infty a_nz^n$ in the unit disk $|z| < 1$, in which we replace the coefficients $a_n$ $(n= 0,1,\ldots ,N)$ of the power…

Complex Variables · Mathematics 2020-04-21 Seraj A. Alkhaleefah , Ilgiz R. Kayumov , Saminathan Ponnusamy

In this article, we analyze refined and improved versions of the classical Bohr inequality for the function class $\mathcal{B}$, which consists of analytic self-mappings defined on the unit disk $\mathbb{D}$. We improve the Bohr-Rogosinski…

Complex Variables · Mathematics 2025-12-19 Molla Basir Aahmed , Partha Pratim Roy

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 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

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…

Complex Variables · Mathematics 2024-02-27 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

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…

Complex Variables · Mathematics 2023-12-27 Molla Basir Ahamed , Sabir Ahammed

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 paper, we first obtain a refined Bohr radius for invariant families of bounded analytic functions on unit disk $ \mathbb{D} $. Then, we obtain Bohr inequality for certain integral transforms, namely Fourier (discrete) and Laplace…

Complex Variables · Mathematics 2024-05-08 Molla Basir Ahamed , Partha Pratim Roy , Sabir Ahammed

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.

Complex Variables · Mathematics 2021-04-15 Saminathan Ponnusamy , Ramakrishnan Vijayakumar

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
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