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Related papers: A note on the Bohr inequality

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In this article, we study the multi-dimensional Bohr radii of holomorphic functions defined on the Banach sequence spaces with values in the Banach spaces. For the case of finite dimensional Banach spaces, we exhibit the exact asymptotic…

Functional Analysis · Mathematics 2023-03-31 Shankey Kumar , Ramesh Manna

In this paper, we aim to establish a range of numerical radius inequalities. These discoveries will bring us to a recently validated numerical radius inequality and will present numerical radius inequalities that exhibit enhanced precision…

Functional Analysis · Mathematics 2024-10-07 M. H. M. Rashid

This article deals with the sharp discrete isoperimetric inequalities in analysis and geometry for planar convex polygons. First, the analytic isoperimetric inequalities based on Schur convex function are established. In the wake of the…

Differential Geometry · Mathematics 2023-06-28 Chunna Zeng , Xu Dong

In this work, an extension of the generalized mixed Schwarz inequality is proved. A companion of the generalized mixed Schwarz inequality is established by merging both Cartesian and Polar decompositions of operators. Based on that some…

Functional Analysis · Mathematics 2018-11-06 Mohammad W. Alomari

The paper establishes a new family of sharp analytic inequalities. Together with the fractional Sobolev inequalities of Almgren and Lieb, they form a complete class of analytic inequalities, referred to as the chord Sobolev inequalities. A…

Metric Geometry · Mathematics 2026-05-12 Fernanda M. Baêta , Xiaxing Cai

In this article we discuss a generalized Wirtinger inequality.

Analysis of PDEs · Mathematics 2010-05-04 Gisella Croce , Bernard Dacorogna

The aim of this work is to expose some asymptotic series associated to some expressions involving the volume of the n-dimensional unit ball. All proofs and the methods used for improving the classical inequalities announced in the final…

Classical Analysis and ODEs · Mathematics 2015-01-08 Cristinel Mortici

Considering some parameters and by means of an inequality of Hadamard, we derive general half-discrete Hilbert-type inequalities. Then we highlight some special cases.

Functional Analysis · Mathematics 2016-01-06 Waleed Abuelela

In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined.

Classical Analysis and ODEs · Mathematics 2010-07-12 Feng Qi , Bai-Ni Guo

In this paper, we prove several sharp Bohr-type and Bohr-Rogosinski-type inequalities for $K$-quasiconformal, sense-preserving harmonic mappings on $\mathbb{D}$, whose analytic part is subordinate to a function belonging to the class of…

Complex Variables · Mathematics 2025-08-04 Molla Basir Ahamed , Taimur Rahman

The purpose of this survey is to give a comprehensive introduction to some classes of classical and recent analytic inequalities in Inner Product Spaces.

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

[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…

Differential Geometry · Mathematics 2024-11-13 Shouvik Datta Choudhury

We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools from Convex Geometry. In this paper we prove a (sharp)…

Functional Analysis · Mathematics 2011-07-13 David Alonso-Gutiérrez , Jesús Bastero , Julio Bernués

In this article we derive some polynomial inequalities for Mertens functions.

Number Theory · Mathematics 2019-02-11 R. Balasubramanian , S. Ponnusamy , K. -J. Wirths

We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…

Optimization and Control · Mathematics 2014-05-13 Tatiana Odzijewicz , Delfim F. M. Torres

In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…

Optimization and Control · Mathematics 2015-03-19 José Matias , Marco Morandotti

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

This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…

Functional Analysis · Mathematics 2025-06-24 Dmytro Seliutin

The higher order analogue of the classical Carath\'eodory-Julia theorem on boundary angular derivatives has been obtained in \cite{bk3}. Here we study boundary interpolation problems for Schur class functions (analytic and bounded by one in…

Classical Analysis and ODEs · Mathematics 2007-05-23 Vladimir Bolotnikov , Alexander Kheifets

The object of this paper is to study the powered Bohr radius $\rho_p$, $p \in (1,2)$, of analytic functions $f(z)=\sum_{k=0}^{\infty} a_kz^k$ and such that $|f(z)|<1$ defined on the unit disk $|z|<1$. More precisely, if $M_p^f…

Complex Variables · Mathematics 2018-09-05 Ilgiz R Kayumov , Saminathan Ponnusamy