Reciprocally convex functions
| Autor: | Milan Merkle |
|---|---|
| Rok vydání: | 2004 |
| Předmět: |
Convex analysis
Convex hull Applied Mathematics Logarithmically concave function Convex set Proper convex function Subderivative Reciprocal convexity Combinatorics Convexity Logarithmically convex function Gamma function Stieltjes transform Quasi-arithmetic means Convex combination Analysis Mathematical expectation Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 293:210-218 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2003.12.021 |
| Popis: | We say that f is reciprocally convex if x↦f(x) is concave and x↦f(1/x) is convex on (0,+∞). Reciprocally convex functions generate a sequence of quasi-arithmetic means, with the first one between harmonic and arithmetic mean and others above the arithmetic mean. We present several examples related to the gamma function and we show that if f is a Stieltjes transform, then −f is reciprocally convex. An application in probability is also presented. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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