Reciprocally convex functions |
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Authors: | Milan Merkle |
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Affiliation: | Department of Mathematics, Faculty of Electrical Engineering, P.O. Box 35-54, 11120 Belgrade, Serbia and Montenegro |
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Abstract: | 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. |
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Keywords: | Convexity Reciprocal convexity Quasi-arithmetic means Gamma function Stieltjes transform Mathematical expectation |
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