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

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

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...

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Bibliographic Details
Main Authors: Jianquan Liao, Shanhe Wu, Bicheng Yang
Format: Article
Language:English
Published: MDPI AG 2020-02-01
Series:Mathematics
Subjects:
weight coefficient
euler–maclaurin summation formula
half-discrete hilbert-type inequality
partial sum
variable upper limit integral
Online Access:https://www.mdpi.com/2227-7390/8/2/229
Description
Summary: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.
ISSN:2227-7390

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