Convex combinations, barycenters and convex functions
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The article first shows one alternative definition of convexity in the discrete case. The correlation between barycenters, Jensen's inequality and convexity is studied in the integral case. The Hermite-Hadamard inequality is also obtained as a consequence of a concept of barycenters. Some derived results are applied to the quasi-arithmetic means, and especially to the power means.
convex function, convex combination; barycenter; convex function; Jensen's inequality; quasi-arithmetic mean, convex combination, barycenter, Applied Mathematics, Discrete Mathematics and Combinatorics, Jensen's inequality, quasi-arithmetic mean, Analysis
convex function, convex combination; barycenter; convex function; Jensen's inequality; quasi-arithmetic mean, convex combination, barycenter, Applied Mathematics, Discrete Mathematics and Combinatorics, Jensen's inequality, quasi-arithmetic mean, Analysis
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