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Related papers: Bohr's inequality revisited

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The main aim of this paper is to prove a generalization of the classical Bohr theorem and as an application, we obtain a counterpart of Bohr theorem for the generalized Ces\'aro operator.

Complex Variables · Mathematics 2021-04-06 Ilgiz R Kayumov , Diana M. Khammatova , Saminathan Ponnusamy

The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.

General Mathematics · Mathematics 2020-02-20 Chang-Jian Zhao , Wing Sum Cheung

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 article, we present some new general forms of numerical radius inequalities for Hilbert space operators. The significance of these inequalities follow from the way they extend and refine some known results in this field. Among other…

Functional Analysis · Mathematics 2019-06-21 Mohammad Sababheh , Hamid Reza Moradi

K-frame theory was recently introduced to reconstruct elements from the range of a bounded linear operator K in a separable Hilbert space. This significant property is worthwhile especially in some problems arising in sampling theory. Some…

Functional Analysis · Mathematics 2017-05-30 Fahimeh Arabyani Neyshaburi , Ghadir Mohajeri Minaei , Ehsan Anjidani

In this paper we establish some new Hermite-Hadamard type inequalities for two operator convex functions of selfadjoint operators in Hilbert spaces.

Functional Analysis · Mathematics 2012-07-05 Amir G. Ghazanfari

The classical inequality of Bohr concerning Taylor coeficients of bounded holomorphic functions on the unit disk, has proved to be of significance in answering in the negative the conjecture that if the non-unital von Neumann inequality…

Functional Analysis · Mathematics 2022-01-26 Vern I. Paulsen , Dinesh Singh

We give a general formulation of Jensen's operator inequality for unital fields of positive linear mappings, and we consider different types of converse inequalities.

Operator Algebras · Mathematics 2008-08-11 Frank Hansen , Josip Pecaric , Ivan Peric

In this paper, we first establish a version of multidimensional analogues of the refined Bohr's inequality. Then we establish two versions of multidimensional analogues of improved Bohr's inequality with initial coefficient being zero.…

Complex Variables · Mathematics 2021-03-18 Ming-Sheng Liu , Saminathan Ponnusamy

We generalize several inequalities involving powers of the numerical radius for product of two operators acting on a Hilbert space. For any $A, B, X\in \mathbb{B}(\mathscr{H})$ such that $A,B$ are positive, we establish some numerical…

Functional Analysis · Mathematics 2015-11-09 Mostafa Sattari , Mohammad Sal Moslehian , Takeaki Yamazaki

Matrix versions of some basic convexity inequalities are given. Further results on the same topic are proved in the recent papers on arxiv: 1. Hermitian operators and convex functions, 2. A concavity inequality for symmetric norms, 3.…

Functional Analysis · Mathematics 2007-05-23 Jean-Christophe Bourin

In this article, we explore the celebrated Gr\"{u}ss inequality, where we present a new approach using the Gr\"{u}ss inequality to obtain new refinements of operator means inequalities. We also present several operator Gr\"{u}ss-type…

Functional Analysis · Mathematics 2020-09-17 H. R. Moradi , S. Furuichi , Z. Heydarbeygi , M. Sababheh

Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.

Functional Analysis · Mathematics 2007-05-23 Sever Silvestru Dragomir

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

The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{P}\Delta(0;1_n)$. We also prove two other sharp versions of the Bohr inequality in…

Complex Variables · Mathematics 2025-12-09 Molla Basir Ahamed , Sujoy Majumder , Nabadwip Sarkar , Ming-Sheng Liu

This is a brief review of Lieb-Thirring inequalities for eigenvalues of the Schroedinger operator and lower bounds for the quantum mechanical kinetic energy (and some generalizations) in R^n.

Mathematical Physics · Physics 2007-05-23 Elliott H. Lieb

We make a careful analysis of Bohr's inequality, in the line started by Kayumov and Ponnusamy, where some extra summand (depending on the function) is added in the right-hand side of the inequality. We analyse the inequality when smaller…

Complex Variables · Mathematics 2024-09-27 Mario Guillén , Pablo Sevilla-Peris

Based on a generalization of Bohr's equivalence relation for general Dirichlet series, in this paper we study the sets of values taken by certain classes of equivalent almost periodic functions in their strips of almost periodicity. In…

Complex Variables · Mathematics 2018-01-11 J. M. Sepulcre , T. Vidal

We present several matrix and operator inequalities of Hermite-Hadamard type. We first establish a majorization version for monotone convex functions on matrices. We then utilize the Mond-Pecaric method to get an operator version for convex…

Functional Analysis · Mathematics 2013-04-02 Mohammad Sal Moslehian

In this article, we first establish operator-valued analogues of multidimensional refined Bohr inequality. Then we establish operator-valued analogues of multidimensional improved Bohr inequality with a certain power of the norm of the…

Complex Variables · Mathematics 2023-08-29 Sabir Ahammed , Molla Basir Ahamed