The Jensen inequality in an external formula (Q2914891)
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scientific article; zbMATH DE number 6084713
| Language | Label | Description | Also known as |
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| English | The Jensen inequality in an external formula |
scientific article; zbMATH DE number 6084713 |
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The Jensen inequality in an external formula (English)
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21 September 2012
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Jensen inequality
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operator concave
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Davis-Choi-Jensen inequality
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reverse inequality
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The classical Jensen inequality is expressed by internally dividing points (e.g., \(x, y, (1-r)x+ry\)). Inspired by \textit{J. I. Fujii} [Sci. Math. Jpn. 73, No. 2--3, 125--128 (2011; Zbl 1233.47011)] and considering externally dividing points (e.g., \(x, y, (1+r)x-ry\)), the authors investigate a vector state version and a Davis--Choi--Jensen type version of the Jensen inequality and its reverse.
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