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Approximating the finite Hilbert transform via some companions of Ostrowski’s inequalities. (English) Zbl 1355.26030

Summary: The finite Hilbert transform is a helpful tool in fields like aerodynamics, the theory of elasticity, and other areas of the engineering sciences. In this paper, by using some companions of Ostrowski’s inequalities for absolutely continuous functions due to Dragomir, we give some new inequalities and approximations for the finite Hilbert transform, which may have the better error bounds than the known results.

MSC:

26D15 Inequalities for sums, series and integrals
26A46 Absolutely continuous real functions in one variable
41A80 Remainders in approximation formulas
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