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In this article, Bohr type inequalities for some complex valued harmonic functions defined on the unit disk are given. All the results are sharp.

Complex Variables · Mathematics 2025-02-06 Jianying Zhou , Wanqing Hou , Boyong Long

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

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

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

The classical Hormander's inequality for linear partial differential operators with constant coeffcients is extended to pseudodifferential operators.

Analysis of PDEs · Mathematics 2007-05-23 Chikh Bouzar

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

In this paper, first we give a new generalization of the Bohr's inequality for the class of bounded analytic functions $\mathcal{B'}$ and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\overline{g},$…

Complex Variables · Mathematics 2021-04-14 Ramakrishnan Vijayakumar

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

In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…

Functional Analysis · Mathematics 2013-11-05 Szilárd László

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

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

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 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, we study the existence of solutions of some kinds of operator equations via operator inequalities. First, we investigate characterizations of operator order $A\geqslant B >0$ and chaotic operator order log $A \geqslant$ log…

Functional Analysis · Mathematics 2011-08-16 Jian Shi , Zongsheng Gao

Let $ \mathcal{H}(\Omega) $ be the class of complex-valued functions harmonic in $ \Omega\subset\mathbb{C} $ and each $f=h+\overline{g}\in \mathcal{H}(\Omega)$, where $ h $ and $ g $ are analytic. In the study of Bohr phenomenon for certain…

Complex Variables · Mathematics 2024-02-20 Molla Basir Ahamed , Partha Pratim Roy

The main aim of this book is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator…

Functional Analysis · Mathematics 2012-03-09 Silvestru Sever Dragomir

The concept of Bohr radius for the class of bounded analytic functions was introduced by Harald Bohr in 1914. His initial result received greater interest and was sharpened-refined-generalized by several mathematicians in various…

Complex Variables · Mathematics 2021-04-14 Saminathan Ponnusamy , Ramakrishnan Vijayakumar , Karl-Joachim Wirths

Given two arbitrary almost periodic functions with associated Fourier exponents which are linearly independent over the rational numbers, we prove that the existence of a common open vertical strip $V$, where both functions assume the same…

Classical Analysis and ODEs · Mathematics 2021-05-04 M. Righetti , J. M. Sepulcre , T. Vidal

In this article, we study the Bohr type inequality for {C}es\'{a}ro operator and {B}ernardi integral operator acting on the space of analytic functions defined on a simply connected domain containing the unit disk $\mathbb{D}$.

Complex Variables · Mathematics 2022-02-15 Vasudevarao Allu , Nirupam Ghosh

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