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Inequalities for a multiple integral. (English) Zbl 0963.26008

Summary: Using Taylor’s formula for functions of several variables, the author establishes inequalities for the integral of a function defined on an \(m\)-dimensional rectangle, if the partial derivatives remain between bounds. Hence Iyengar’s inequality [K. S. K. Iyengar, Math. Student 6, 75-76 (1938)] and related results in the references can be deduced.

MSC:

26D15 Inequalities for sums, series and integrals
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