A Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums

In this paper, we establish a new Hardy–Hilbert-type inequality involving parameters composed of a pair of weight coefficients with their sum. Our result is a unified generalization of some Hardy–Hilbert-type inequalities presented in earlier papers. Based on the obtained inequality, the equivalent...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Bicheng Yang, Shanhe Wu, Xingshou Huang
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	weight coefficients Hardy–Hilbert-type inequality Euler–Maclaurin summation formula equivalent conditions operator expressions Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/8a593e2ea9d240b2a3e8a5e210c53f50
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:8a593e2ea9d240b2a3e8a5e210c53f50
record_format	dspace
spelling	oai:doaj.org-article:8a593e2ea9d240b2a3e8a5e210c53f502021-11-25T18:17:28ZA Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums10.3390/math92229502227-7390https://doaj.org/article/8a593e2ea9d240b2a3e8a5e210c53f502021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2950https://doaj.org/toc/2227-7390In this paper, we establish a new Hardy–Hilbert-type inequality involving parameters composed of a pair of weight coefficients with their sum. Our result is a unified generalization of some Hardy–Hilbert-type inequalities presented in earlier papers. Based on the obtained inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed, and the equivalent forms and the operator expressions are also considered. As applications, we illustrate how the inequality obtained can generate some new Hardy–Hilbert-type inequalities.Bicheng YangShanhe WuXingshou HuangMDPI AGarticleweight coefficientsHardy–Hilbert-type inequalityEuler–Maclaurin summation formulaequivalent conditionsoperator expressionsMathematicsQA1-939ENMathematics, Vol 9, Iss 2950, p 2950 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	weight coefficients Hardy–Hilbert-type inequality Euler–Maclaurin summation formula equivalent conditions operator expressions Mathematics QA1-939
spellingShingle	weight coefficients Hardy–Hilbert-type inequality Euler–Maclaurin summation formula equivalent conditions operator expressions Mathematics QA1-939 Bicheng Yang Shanhe Wu Xingshou Huang A Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums
description	In this paper, we establish a new Hardy–Hilbert-type inequality involving parameters composed of a pair of weight coefficients with their sum. Our result is a unified generalization of some Hardy–Hilbert-type inequalities presented in earlier papers. Based on the obtained inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed, and the equivalent forms and the operator expressions are also considered. As applications, we illustrate how the inequality obtained can generate some new Hardy–Hilbert-type inequalities.
format	article
author	Bicheng Yang Shanhe Wu Xingshou Huang
author_facet	Bicheng Yang Shanhe Wu Xingshou Huang
author_sort	Bicheng Yang
title	A Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums
title_short	A Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums
title_full	A Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums
title_fullStr	A Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums
title_full_unstemmed	A Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums
title_sort	hardy–hilbert-type inequality involving parameters composed of a pair of weight coefficients with their sums
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/8a593e2ea9d240b2a3e8a5e210c53f50
work_keys_str_mv	AT bichengyang ahardyhilberttypeinequalityinvolvingparameterscomposedofapairofweightcoefficientswiththeirsums AT shanhewu ahardyhilberttypeinequalityinvolvingparameterscomposedofapairofweightcoefficientswiththeirsums AT xingshouhuang ahardyhilberttypeinequalityinvolvingparameterscomposedofapairofweightcoefficientswiththeirsums AT bichengyang hardyhilberttypeinequalityinvolvingparameterscomposedofapairofweightcoefficientswiththeirsums AT shanhewu hardyhilberttypeinequalityinvolvingparameterscomposedofapairofweightcoefficientswiththeirsums AT xingshouhuang hardyhilberttypeinequalityinvolvingparameterscomposedofapairofweightcoefficientswiththeirsums
_version_	1718411394189099008

A Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums

Ejemplares similares