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On a New Extended Hardy–Hilbert’s Inequality with Parameters
Open AccessArticle

On a New Half-Discrete Hilbert-Type Inequality Involving the Variable Upper Limit Integral and Partial Sums

1
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, China
2
Department of Mathematics, Longyan University, Longyan, Fujian 364012, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 229; https://doi.org/10.3390/math8020229
Received: 5 January 2020 / Revised: 5 February 2020 / Accepted: 7 February 2020 / Published: 10 February 2020
(This article belongs to the Special Issue Inequalities 2020)
In this paper we establish a new half-discrete Hilbert-type inequality involving the variable upper limit integral and partial sums. As applications, an inequality obtained from the special case of the half-discrete Hilbert-type inequality is further investigated; moreover, the equivalent conditions of the best possible constant factor related to several parameters are proved.
Keywords: weight coefficient; Euler–Maclaurin summation formula; half-discrete Hilbert-type inequality; partial sum; variable upper limit integral weight coefficient; Euler–Maclaurin summation formula; half-discrete Hilbert-type inequality; partial sum; variable upper limit integral
MDPI and ACS Style

Liao, J.; Wu, S.; Yang, B. On a New Half-Discrete Hilbert-Type Inequality Involving the Variable Upper Limit Integral and Partial Sums. Mathematics 2020, 8, 229.

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