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Note on inequalities involving integral Taylor’s remainder. (English) Zbl 1087.26014

By using certain classical methods (Leibniz formula, Grüss inequality, Steffensen inequality), the author offers new proofs, as well as improvements for certain inequalities involving Taylor’s remainder, due to L. Bougoffa [JIPAM, J. Inequal. Pure Appl. Math. 4, No. 5, Paper No. 86, 4 p. (2003; Zbl 1072.26009)] and H. Gauchman [JIPAM, J. Inequal. Pure Appl. Math. 4, No. 1, Paper No. 1, 5 p. (2003; Zbl 1032.26015)].

MSC:

26D15 Inequalities for sums, series and integrals
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