On some inequality of Hermite-Hadamard type
Copyright policy )On some inequality of Hermite-Hadamard type
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 Fejer type.
Submitted to Opuscula Math
convex function, T57-57.97, Applied mathematics. Quantitative methods, Functional Analysis (math.FA), Mathematics - Functional Analysis, approximate integration, Hermite-Hadamard inequality, Fejér inequality, Mathematics - Classical Analysis and ODEs, 26D15 (Primary) 26A51, 26B25, 65D30, 65D32 (Secondary), Classical Analysis and ODEs (math.CA), FOS: Mathematics, simplex
convex function, T57-57.97, Applied mathematics. Quantitative methods, Functional Analysis (math.FA), Mathematics - Functional Analysis, approximate integration, Hermite-Hadamard inequality, Fejér inequality, Mathematics - Classical Analysis and ODEs, 26D15 (Primary) 26A51, 26B25, 65D30, 65D32 (Secondary), Classical Analysis and ODEs (math.CA), FOS: Mathematics, simplex
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