Related papers: The Bohr radius and the Hadamard convolution opera…
In this article we establish Bohr inequalities for operator valued functions, which can be viewed as the analogues of a couple of interesting results from scalar valued settings. Some results of this paper are motivated by the classical…
In this article, the new inequalities for the weighted sums of coefficients in the class of bounded functions in the disk are obtained. We develop the methods of I.R.~Kayumov and S.~Ponnusamy, using E.~Reich's theorem on the majorization of…
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…
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…
In this paper, we investigate the arithmetic Bohr radius of bounded linear operators between arbitrary complex Banach spaces. We establish the close connection between the classical Bohr radius and the arithmetic Bohr radius of bounded…
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…
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.
Multivariable operator theory is used to provide Bohr inequalities for free holomorphic functions with operator coefficients on the regular polyball. In addition, we obtain analogues of Caratheodory, Fejer, and Egervary-Szazs inequalities…
The purpose of this article is to study Bohr inequalities involving the absolute values of the coefficients of an operator valued function. To be more specific, we establish an operator valued analogue of a classical result regarding the…
We give an expression for a generalized numerical radius of Hilbert space operators and then apply it to obtain upper and lower bounds for the generalized numerical radius. We also establish some generalized numerical radius inequalities…
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…
Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.
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…
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…
This paper introduces the second Bohr radius for vector-valued holomorphic functions defined on arbitrary complete Reinhardt domains. We aim to establish the lower and upper bounds of the second Bohr radius in both finite and…
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…
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…
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…
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.
In this article, we present some new inequalities for numerical radius of Hilbert space operators via convex functions. Our results generalize and improve earlier results by El-Haddad and Kittaneh. Among several results, we show that if…