English
Related papers

Related papers: Bohr inequalities for free holomorphic functions o…

200 papers

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 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

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

Slice regular functions are a generalization of holomorphic functions to the setting of quaternions (and more generally, Clifford algebras). In this paper, we first establish the Bohr inequality for slice starlike functions and slice…

Complex Variables · Mathematics 2025-11-18 Sabir Ahammed , Molla Basir Ahamed , Ming-Sheng Liu

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

In this paper, we prove some operator inequalities associated with an extension of the Kantorovich type inequality for $s$-convex function. We also give an application to the order preserving power inequality of three variables and find a…

Functional Analysis · Mathematics 2022-10-11 Ismail Nikoufar , Davuod Saeedi

In this article, we study the Bohr operator for the operator valued subordination class $S(f)$ consisting of holomorphic functions subordinate to $f$ in the unit disk $\mathbb{D}:=\{z \in \mathbb{C}: |z|<1\}$, where $f:\mathbb{D}…

Complex Variables · Mathematics 2026-04-15 Vasudevarao Allu , Himadri Halder

In this paper, we introduce the concept of operator arithmetic-geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities…

Functional Analysis · Mathematics 2016-03-16 Ali Taghavi , Vahid Darvish , Haji Mohammad Nazari

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

In this article we prove Bohr inequalities for sense-preserving $K$-quasiconformal harmonic mappings defined in $\mathbb{D}$ and obtain the corresponding results for sense-preserving harmonic mappings by letting $K\to\infty$. One of the…

Complex Variables · Mathematics 2021-01-12 Bappaditya Bhowmik , Nilanjan Das

This paper is an attempt to find large classes of noncommutative multivariable functions $g:\Omega\subset [B(\cH)^n]_1^-\to B(\cH)^n$ for which a reasonable operator model theory and dilation theory can be developed for the noncommutative…

Functional Analysis · Mathematics 2011-11-23 Gelu Popescu

In this paper we continue the study of free holomorphic functions on the unit ball of B(H)^n, where B(H) is the algebra of all bounded linear operators on a Hilbert space H. Several classical results from complex analysis have free…

Functional Analysis · Mathematics 2009-11-29 Gelu Popescu

We establish an operator extension of the following generalization of Bohr's inequality, due to M.P. Vasi\'c and D.J. Ke\v{c}ki\'{c}: $$|\sum_{i=1}^n z_i|^r \leq (\sum_{i=1}^n \alpha_i^{1/(1-r)})^{r-1}\sum_{i=1}^n \alpha_i|z_i|^r \quad…

Operator Algebras · Mathematics 2010-05-31 M. S. Moslehian , J. Pecaric , I. Peric

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

In this paper, several Bohr-type inequalities are generalized to the form with two parameters for the bounded analytic function. Most of the results are sharp.

Complex Variables · Mathematics 2025-02-06 Wanqing Hou , Qihan Wang , Boyong Long

We determine the Bohr radius for the class of all functions $f$ of the form $f(z)=\sum_{k=1}^\infty a_{kp+m} z^{kp+m}$ analytic in the unit disk $|z|<1$ and satisfy the condition $|f(z)|\le 1$ for all $|z|<1$. In particular, our result also…

Complex Variables · Mathematics 2017-08-21 Ilgiz R Kayumov , Saminathan Ponnusamy

In this paper, we derive a generalized multiplicative Hardy-Littlewood-Polya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of…

Functional Analysis · Mathematics 2015-10-06 Vladyslav Babenko , Yuliya Babenko , Nadiia Kriachko

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

In this paper, we investigate several Bohr radii associated with the Ces\'aro operator, Bernardi integral operator, $\beta$-Ces\'aro operator, and discrete Fourier transform, all defined on a set of holomorphic mappings from the unit ball…

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

We give necessary and sufficient conditions for two weight norm inequalities for Haar multipliers operators and for square functions. We also give sufficient conditions for two weight norm inequalities for the Hilbert transform.

Functional Analysis · Mathematics 2009-09-25 Fedor Nazarov , Sergei Treil , Alexander Volberg