Abstract
Jensen’s inequality in its original form says that if f is a scalar convex function (on an open convex set, A, of a vector space, V) and if \(\{x_j\}_{j=1}^n \subset A; \, 0 \le \theta _j \le 1, \, j=1,\dots ,n\) with \(\sum _{j=1}^n \theta _j = 1\), then \(f(\sum _{j=1}^n \theta _j x_j) \le \sum _{j=1}^n \theta _j f(x_j)\).
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Simon, B. (2019). Convexity, III: Hansen–Jensen–Pedersen (HJP) Inequality. In: Loewner's Theorem on Monotone Matrix Functions. Grundlehren der mathematischen Wissenschaften, vol 354. Springer, Cham. https://doi.org/10.1007/978-3-030-22422-6_11
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DOI: https://doi.org/10.1007/978-3-030-22422-6_11
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