Christophe Chesneau

On Two One-Parameter Variants of the Hardy-Hilbert Integral Inequality

Christophe Chesneau, Josip E. Pečarić

This article establishes two new one-parameter variants of the Hardy-Hilbert integral inequality. These results are derived by modifying an existing framework that incorporates the absolute difference between unity and the product of two variables, raised to an adjustable power parameter. By employing …

fr, hr (code pays fourni par la source)

Examining Two New Hardy-Hilbert-Type Integral Inequalities

Christophe Chesneau

This article investigates two Hardy-Hilbert-type integral inequalities. The first inequality involves a parameter that introduces analytical flexibility and affects only the constant factor in the upper bound. This constant is expressed explicitly in terms of the beta function, emphasizing the simplicity and …

Study of an extended trivariate Hilbert integral inequality

Christophe Chesneau

In this paper, we establish a new integral inequality that extends the scope of the classical trivariate Hardy-Hilbert integral inequality. The main contributions are (i) to generalize a famous result in the literature with the use of additional adaptable functions and parameters, …

Variants of the Damascus inequality

Chanatip Sujsuntinukul, Christophe Chesneau

In 2016, Dannan and Sitnik established the notable Damascus inequality, which features a symmetric structure under a multiplicative constraint. In this study, we consider the natural generalisation of this inequality by characterising all positive integers $m$ and $n$ such that the inequality …

SOME NEW CONVEX INTEGRAL INEQUALITIES INVOLVING TWO FUNCTIONS

Christophe Chesneau

This article investigates new integral inequalities involving two functions under convexity assumptions. Specifically, we derive upper and lower bounds for two different integral forms using techniques based on the convexity inequality, as well as the Jensen and Chebyshev integral inequalities. The results …

REVISITING TWO VARIANTS OF THE HARDY-HILBERT INTEGRAL INEQUALITY

Christophe Chesneau

The Hardy-Hilbert integral inequality is fundamental to mathematical analysis. It has inspired a vast body of research devoted to its generalizations and refinements. This article sheds new light on the subject by demonstrating that certain variants of the inequality possess a self-extending …

New Young-type integral inequalities using composition schemes

Christophe Chesneau

Abstract This article presents new results that extend the scope of the Young integral inequality. They are formulated by different functional composition schemes of the integrals involved. These schemes depend on a unique auxiliary function. In total, six theorems are proved. Four …

fr (code pays fourni par la source)

Novel weighted distribution: Properties, applications and web-tool

Emrah Altun, Christophe Chesneau

Abstract Weighted distributions play an important role in reliability and engineering. This research contributes to the topic by presenting a novel flexible two-parameter weighted distribution characterized by extensive statistical properties. Various parameter estimation methods are also thoroughly investigated. Their effectiveness is validated …

tr, fr (code pays fourni par la source)

New Results for the Hardy Integral Inequality Based on the Change of Variables Point of View

Christophe Chesneau

The Hardy integral inequality is a key result in analysis and plays an important role in many areas of mathematics. It has been proved in various ways, including a direct one combining a change of variables and the Minkowski integral inequality. However, …

fr (code pays fourni par la source)

A Note on an Original Lifetime Distribution

Christophe Chesneau

This article introduces a new lifetime distribution with an original probability density function that is governed by two parameters. This distribution can be considered a modification of the exponential distribution. A theoretical investigation of its main properties is conducted, and key functions …

fr (code pays fourni par la source)

Extension and Correction of an Inequality Similar to the Hardy-Hilbert Integral Inequality

Christophe Chesneau

In this article, we present an extension to the Hardy-Hilbert integral inequality. This extension incorporates a multivariate parametric power-ratio function. The original formulation of the inequality is also included, along with a correction.

fr (code pays fourni par la source)

Hilbert-type integral inequalities based on the hyperbolic tangent function

Christophe Chesneau

The Hilbert integral inequality is a well-established result in mathematical analysis and has given rise to an interesting line of research.In this article, two new variants of the Hilbert integral inequality are presented, both derived from the hyperbolic arctangent function.In the first …

fr (code pays fourni par la source)