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Zbl 0981.26014
Duoandikoetxea, Javier
A unified approach to several inequalities involving functions and derivatives. (English)
[J] Czech. Math. J. 51, No.2, 363-376 (2001). ISSN 0011-4642; ISSN 1572-9141/e

Summary: There are many inequalities measuring the deviation of the average of a function over an interval from a linear combination of values of the function and some of its derivatives. A general setting is given from which the desired inequalities are obtained using Hölder's inequality. Moreover, sharpness of the constants is usually easy to prove by studying the equality cases of Hölder's inequality. Comparison of averages, extension to weighted integrals and $n$-dimensional results are also given.

MSC 2000:: *26D10 Inequalities involving derivatives, diff. and integral operators
26D15 Inequalities for sums, series and integrals of real functions

Keywords: inequalities; averages of functions; quadrature; weighted integrals

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