A more accurate half-discrete Hilbert-type inequality involving one higher-order derivative function. (English) Zbl 07885466
Summary: By means of the weight functions, Hermite-Hadamards inequality and the techniques of real analysis, a new more accurate half-discrete Hilberttype inequality involving one higher-order derivative function is given. The equivalent conditions of the best possible constant factor related to a few parameters, the equivalent forms, several particular inequalities and the operator expressions are considered.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 26A42 | Integrals of Riemann, Stieltjes and Lebesgue type |
Keywords:
weight function; Hermite-Hadamards inequality; half-discrete Hilbert-type inequality; higher-order derivative function; parameter; best possible constant factorReferences:
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