The Hermite-Hadamard inequality for convex functions on a global NPC space |
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Authors: | Constantin P. Niculescu |
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Affiliation: | University of Craiova, Department of Mathematics, Craiova 200585, Romania |
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Abstract: | We prove an extension of Choquet's theorem to the framework of compact metric spaces with a global nonpositive curvature. Together with Sturm's extension [K.T. Sturm, Probability measures on metric spaces of nonpositive curvature, in: Pascal Auscher, et al. (Eds.), Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces, Lecture Notes from a Quarter Program on Heat Kernels, Random Walks, and Analysis on Manifolds and Graphs April 16-July 13, 2002, Paris, France, in: Contemp. Math., vol. 338, Amer. Math. Soc., Providence, RI, 2003, pp. 357-390] of Jensen's inequality, this provides a full analogue of the Hermite-Hadamard inequality for the convex functions defined on such spaces. |
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Keywords: | Global NPC space Extreme point Convex function |
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