A Hardy-Hilbert-type inequality involving modified weight coefficients and partial sums

Abstract

<abstract> <p>In this article, we construct proper weight coefficients and use them to establish a Hardy-Hilbert-type inequality involving one partial sum. Based on this inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed. We also consider the equivalent forms and the operator expressions of the obtained inequalities. At the end of the paper, we demonstrate that more new Hardy-Hilbert-type inequalities can be derived from the special cases of the present results.</p> </abstract>

A Weighted Generalization of Hardy–Hilbert-Type Inequality Involving Two Partial Sums

“…Inspired by the aforementioned studies [3][4][5][6], in this article, we construct a new weighted generalized version of Hardy-Hilbert inequality involving two partial sums, which has a different configuration of weight coefficients compared with the above inequalities (3)- (6). At the end of the paper, we show that our main finding is a generalization of the above-mentioned results obtained by Adiyasuren et al [3].…”

“…Huang, Wu and Yang [4] established an analogous version of inequality (3), which contains one partial sum B n and three parameters η, η 1 , η 2 .…”