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.
Refinement of the right-hand side of Hermite-Hadamard inequality for simplices
A solution to an open problem on the Mathieu series posed by Hoorfar and Qi
A refinement of the left-hand side of Hermite-Hadamard inequality for simplices
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