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Related papers: Inequalities involving arithmetic functions

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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…

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

Socio-economic inequalities are manifested in different aspects of our social life. We discuss various aspects, beginning with the evolutionary and historical origins, and discussing the major issues from the social and economic point of…

Physics and Society · Physics 2016-02-02 Arnab Chatterjee

In this paper we present some inequalities involving operator decreasing functions and operator means. These inequalities provide some reverses of operator Acz\'el inequality dealing with the weighted geometric mean.

Functional Analysis · Mathematics 2018-04-17 Venus Kaleibary , Shigeru Furuichi

We aim to introduce a $\mathtt{k}$-Struve function and investigate its various properties, including mainly certain inequalities associated this function. One of the inequalities given here is pointed out to be related to the so-called…

Classical Analysis and ODEs · Mathematics 2016-11-29 Kottakkaran Sooppy Nisar , Saiful Rahman Mondal , Junesang Choi

In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and H\" older type functions etc. These results give us an elegant method for…

Functional Analysis · Mathematics 2016-12-02 Mea Bombardelli , Ludmila Nikolova , Sanja Varošanec

In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…

Differential Geometry · Mathematics 2019-09-18 Lashi Bandara

Bernoulli type inequalities for functions of logarithmic type are given. These functions include, in particular, Gaussian hypergeometric functions in the zero-balanced case $F(a,b;a+b;x)\,.$

Classical Analysis and ODEs · Mathematics 2016-05-30 Riku Klén , Vesna Manojlović , Slavko Simić , Matti Vuorinen

There exist two major subclasses in the class of superquadratic functions, one comprises concave and decreasing functions, while the other consists of convex and monotone increasing functions. Leveraging this distinction, we introduce…

Functional Analysis · Mathematics 2024-03-19 Mohsen Kian

We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…

Algebraic Geometry · Mathematics 2015-08-10 Yuhan Zha

A Compact Introduction to Fractional Calculus is presented including basic definitions, fractional differential equations and special functions.

History and Overview · Mathematics 2023-01-03 Alexander I. Zhmakin

We consider the problem of evaluating certain types of functional aggregation queries on relational data subject to additive inequalities. Such aggregation queries, with a smallish number of additive inequalities, arise naturally/commonly…

Data Structures and Algorithms · Computer Science 2020-05-04 Mahmoud Abo-Khamis , Sungjin Im , Benjamin Moseley , Kirk Pruhs , Alireza Samadian

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

In this paper, we study Bohr's inequality and refined versions of Bohr-Rogosinski inequalities involving Schwarz functions. Moreover, we establish a version of multidimensional analogue of Bohr inequality and Bohr-Rogosinski inequalities…

Complex Variables · Mathematics 2023-12-12 Sabir Ahammed , Molla Basir Ahamed

This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the additive canon. Of particular interest are problems about the…

Number Theory · Mathematics 2026-04-23 Melvyn B. Nathanson

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 article we discuss a generalized Wirtinger inequality.

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

Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.

Mathematical Physics · Physics 2014-06-30 V. I. Man'ko , L. A. Markovich

The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional $p-$Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and…

Classical Analysis and ODEs · Mathematics 2013-09-20 Riku Klén , Matti Vuorinen , Xiaohui Zhang

The main goal of this article is to present several quadratic refinements and reverses of the well known Heinz inequality, for numbers and matrices, where the refining term is a quadratic function in the mean parameters. The proposed idea…

Functional Analysis · Mathematics 2021-07-23 Fuad Kittaneh , Mohammad Sal Moslehian , Mohammad Sababheh

The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to…

Combinatorics · Mathematics 2021-01-18 Piotr Pokora