A new reverse half-discrete Mulholland-type inequality with a nonhomogeneous kernel

Journal of Inequalities and Applications

Research

Bicheng Yang¹  Ling Peng²  Rahela Abd Rahim³ 

[1] School of Mathematics, Guangdong University of Education, 510303, Guangzhou, Guangdong, P.R. China;School of Medical Humanity and Information Management, Hunan University of Medicine, 418000, Huaihua, Hunan, P.R. China;School of Quantitative Sciences, University Utara Malaysia, 06010, Sintok, Kedah, Malaysia;School of Quantitative Sciences, University Utara Malaysia, 06010, Sintok, Kedah, Malaysia;

关键词: Mulholland-type inequality;    Parameter;    Weight function;    Best possible constant factor;    Reverse;    26D15;   

DOI  :  10.1186/s13660-023-03025-w

 received in 2023-01-15, accepted in 2023-08-29,  发布年份 2023

来源: Springer

【 摘 要 】

In this paper, a new reverse half-discrete Mulholland-type inequality with the nonhomogeneous kernel of the form h(v(x)lnn)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$h(v(x)\ln n)$\end{document} and the best possible constant factor is obtained by using the weight functions and the technique of real analysis. The equivalent reverses are considered. As corollaries, we deduce some new equivalent reverse inequalities with the homogeneous kernel of the form kλ(v(x),lnn)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$k_{\lambda }(v(x),\ln n)$\end{document}. A few particular cases are provided. Our new reverse half-discrete Mulholland-type inequality which has a nonhomogeneous kernel is more general than in the previous homogeneous kernel work. The harmonized integration will have more applications.

【 授权许可】

CC BY   
© Springer Nature Switzerland AG 2023

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