Opuscula Math. 32, no. 3 (2012), 591-600
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.
About the authors ▼
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
About the article ▼
Received: 2011-09-29.
Accepted: 2011-12-30.
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.
Download this article's citation as: