ON A NEW HALF-DISCRETE HILBERT-TYPE INEQUALITY WITH THE MULTIPLE UPPER LIMIT FUNCTION AND THE PARTIAL SUMS

ON A NEW HALF-DISCRETE HILBERT-TYPE INEQUALITY WITH THE MULTIPLE UPPER LIMIT FUNCTION AND THE PARTIAL SUMS

By means of the weight coefficients, the Euler-Maclaurin summation formula and Abel’s summation by parts formula, a new half-discrete Hilbert-type inequality with the power function as the interval variables as well as one multiple upper limit function and one partial sums is given. As applications,...

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Bibliographic Details
Main Authors: Wang, A. (Author), Yang, B. (Author), Yong, H. (Author)
Format: Article
Language:English
Published: Wilmington Scientific Publisher 2022
Subjects:
Euler-Maclaurin summation formula
Half-dis-crete Hilbert-type inequality
multiple upper limit function
parameter
partial sums
Weight coefficient
Online Access:View Fulltext in Publisher
Description
Summary:By means of the weight coefficients, the Euler-Maclaurin summation formula and Abel’s summation by parts formula, a new half-discrete Hilbert-type inequality with the power function as the interval variables as well as one multiple upper limit function and one partial sums is given. As applications, the equivalent conditions of the best possible constant factor in a particular inequality related to a few parameters and some particular cases are considered. We also obtain the equivalent forms and the operator expression in the case of m = 0. © 2022, Wilmington Scientific Publisher. All rights reserved.
ISBN:2156907X (ISSN)
DOI:10.11948/20210423

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