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Zbl 1043.26012
Kirmaci, U.S.; Özdemir, M.E.
On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula. (English)
[J] Appl. Math. Comput. 153, No. 2, 361-368 (2004). ISSN 0096-3003

Summary: Some inequalities are presented here for differentiable convex mappings, using Hermite-Hadamard's integral inequality holding for convex functions. A parallel development is deduced for differentiable concave functions. Some applications to special means of real numbers are also given. Finally, some error estimates for the midpoint formula are obtained.

MSC 2000:: *26D15 Inequalities for sums, series and integrals of real functions
26A51 Convexity, generalizations (one real variable)
26E60 Means

Keywords: Hermite--Hadamard inequality; convex functions; concave functions; special means; midpoint formula; integral inequalities

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