Opuscula Math. 32, no. 3 (2012), 591-600

Opuscula Mathematica

On some inequality of Hermite-Hadamard type

Szymon Wąsowicz
Alfred Witkowski

Abstract. It is well-known that the left term of the classical Hermite-Hadamard inequality is closer to the integral mean value than the right one. We show that in the multivariate case it is not true. Moreover, we introduce some related inequality comparing the methods of the approximate integration, which is optimal. We also present its counterpart of Fejér type.

Keywords: convex function, Hermite-Hadamard inequality, Fejér inequality, simplex, approximate integration.

Mathematics Subject Classification: 26D15, 26A51, 26B25, 65D30, 65D32.

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  • Szymon Wąsowicz
  • University of Bielsko-Biała, Department of Mathematics and Computer Science, Willowa 2, 43–309 Bielsko-Biała, Poland
  • Alfred Witkowski
  • University of Technology and Life Sciences, Institute of Mathematics and Physics, al. prof. Kaliskiego 7, 85-796 Bydgoszcz, Poland
  • Received: 2011-09-29.
  • Accepted: 2011-12-30.
Opuscula Mathematica - cover

Cite this article as:
Szymon Wąsowicz, Alfred Witkowski, On some inequality of Hermite-Hadamard type, Opuscula Math. 32, no. 3 (2012), 591-600, http://dx.doi.org/10.7494/OpMath.2012.32.3.591

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