Improvements of the Hermite-Hadamard inequality for the simplex
نویسندگان
چکیده
منابع مشابه
Improvements of the Hermite-Hadamard inequality for the simplex
In this study, the simplex whose vertices are barycenters of the given simplex facets plays an essential role. The article provides an extension of the Hermite-Hadamard inequality from the simplex barycenter to any point of the inscribed simplex except its vertices. A two-sided refinement of the generalized inequality is obtained in completion of this work.
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equality holds in either side only for the affine functions (i.e., for the functions of the form mx+ n). The middle point (a + b)/2 represents the barycenter of the probability measure 1 b−adx (viewed as a mass distribution over the interval [a, b]), while a and b represent the extreme points of [a, b]. Thus the Hermite-Hadamard inequality could be seen as a precursor of Choquet’s theory. See [...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2017
ISSN: 1029-242X
DOI: 10.1186/s13660-016-1273-z