Sharp integral inequalities of the Hermite-Hadamard type. (English) Zbl 1012.26013

Guessab, Allal; Schmeisser, Gerhard

J. Approximation Theory 115, No. 2, 260-288 (2002).

Authors’ summary: “We consider a family of two-point quadrature formulae and establish sharp estimates for the remainders under various regularity conditions. Improved forms of certain integral inequalities due to Hermite and Hadamard, Iyengar, Milovanović and Pečarić, and others are obtained as special cases. Our results can also be interpreted as analogues to a theorem of Ostrowski on the deviation of a function from its averages. Furthermore, we establish a generalization of a result of Fink concerning \(L^p\) estimates for the remainder of the trapezoidal rule and present the best constants in the error bounds”.

Reviewer: George A.Anastassiou (Memphis)

MSC:

26D15	Inequalities for sums, series and integrals
65D30	Numerical integration
41A55	Approximate quadratures
65D32	Numerical quadrature and cubature formulas

Keywords:

Hermite-Hadamard inequality; two-point quadrature formulae; integral inequalities; trapezoidal rule

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