A version of the Hermite-Hadamard inequality in a nonpositve curvature space. (English) Zbl 1247.39026
The aim of this paper is to discuss an analogue of the Hermite-Hadamard inequality for convex functions defined on a space with curved geometry, more precisely on a metric space with global nonpositive curvature. The details are however, too involving to be stated here.
Reviewer: József Sándor (Cluj-Napoca)
MSC:
| 39B62 | Functional inequalities, including subadditivity, convexity, etc. |
| 32F17 | Other notions of convexity in relation to several complex variables |
| 54E50 | Complete metric spaces |
| 58B20 | Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds |
| 26D15 | Inequalities for sums, series and integrals |
| 26A51 | Convexity of real functions in one variable, generalizations |
Keywords:
nonpositive curvature metric space; geodesic convexity; Hermite-Hadamard inequality; convex functionsReferences:
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