New Hilbert-type inequality reveals improved accuracy using advanced summation techniques, suggesting refined mathematical analysis methods.
By using the weight coefficients, the Euler-Maclaurin summation formula and Abel summation by parts formula, a new more accurate Hilbert-type inequality with the power function as the internal variables involving one partial sum is given. The equivalent conditions of the best value related to a few parameters are obtained, and some particular inequalities are considered. We also provide the equivalent forms and the operator expressions.
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Wang et al. (2026) studied this question.
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