Journal of Jilin University Science Edition ›› 2023, Vol. 61 ›› Issue (6): 1296-1304.
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WANG Aizhen, YANG Bicheng
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Abstract: Firstly, by using the method of weight functions, Euler-Maclaurin summation formula, Abel’s summation by parts formula, and the technique of real analysis, we gave a new half-discrete Hilbert-type inequality involving higher-order derivative function and partial sums. Secondly, as applications, we discussed the equivalent conditions of the best constant factor to connect multiple parameters in a inequality with particular parameter and several particular inequalities.
Key words: weight function, Euler-Maclaurin summation formula, Abel’s summation by parts formula, half-discrete Hilbert-type inequality, higher-order derivative function, partial sums
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WANG Aizhen, YANG Bicheng. A New Half-Discrete Hilbert-Type Inequality Involving Higher-Order Derivative Function and Partial Sums[J].Journal of Jilin University Science Edition, 2023, 61(6): 1296-1304.
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http://xuebao.jlu.edu.cn/lxb/EN/Y2023/V61/I6/1296
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