On a new class of Hardy-type inequalities

Journal of inequalities and applications

EO Adeleke¹ 

关键词: Hardy inequality;    power weights;    convex functions;    superquadratic functions;   

DOI  :  10.1186/1029-242X-2012-259

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we generalize a Hardy-type inequality to the class of arbitrary non-negative functions bounded from below and above with a convex function multiplied with positive real constants. This enables us to obtain new generalizations of the classical integral Hardy, Hardy-Hilbert, Hardy-Littlewood-Pólya, and Pólya-Knopp inequalities as well as of Godunova’s and of some recently obtained inequalities in multidimensional settings. Finally, we apply a similar idea to functions bounded from below and above with a superquadratic function. MSC: 26D10, 26D15.

【 授权许可】

CC BY