Some refinements of Hermite-Hadamard inequality and an open problem

2016/11/07 by Simic, Slavko
#26D07 (26D15) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.01905

Abstract

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.

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