Geodesic
Some Refinements of Hermite-Hadamard Inequality and an Open Problem
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 3, p. 349 .

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We presented here a refinement of Hermite-Hadamard inequality as a linear combination of its end-points. The problem of best possible constants is closely connected with well known Simpson's rule in numerical integration. It is solved here for a wide class of convex functions, but not in general. Some supplementary results are also given.
Classification : 26D07 26D15
Keywords: Hermite-Hadamard integral inequality, differentiable function, convex function 
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     title = {Some {Refinements} of {Hermite-Hadamard} {Inequality} and an {Open} {Problem}},
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Slavko Simić. Some Refinements of Hermite-Hadamard Inequality and an Open Problem. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 3, p. 349 . http://geodesic.mathdoc.fr/item/KJM_2018_42_3_a2/