Hadamard type inequality for quasiconvex functions in higher dimensions (Q697426)
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scientific article; zbMATH DE number 1801633
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hadamard type inequality for quasiconvex functions in higher dimensions |
scientific article; zbMATH DE number 1801633 |
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Hadamard type inequality for quasiconvex functions in higher dimensions (English)
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17 September 2002
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As was established in [\textit{S. S. Dragomir} and \textit{C. E. M. Pearce}, Bull. Aust. Math. Soc. 57, No.~3, 373-385 (1998; Zbl 0908.26015)] , for a quasiconvex function \(f\) defined on \([a,b]\) we have \[ f\left( \frac{a+b}{2}\right) \leq \frac{2}{b-a}\int_{a}^{b}f(x) dx. \] This Hadamard type inequality is extended here for quasiconvex functions in higher dimensions.
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quasiconvex functions
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Hadamard inequality
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supremal generators
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0.9476417
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0.9326522
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0.93062496
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0.9254675
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