Two-point Ostrowski inequality (Q2720282)
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scientific article; zbMATH DE number 1610906
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two-point Ostrowski inequality |
scientific article; zbMATH DE number 1610906 |
Statements
Two-point Ostrowski inequality (English)
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26 June 2001
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Ostrowski inequality
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integral mean
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The authors improve a ``two-point'' Ostrowski inequality of Barnett and Dragomir, by proving the following result: If \(f:[a, b]\to \mathbb{R}\) is \(M\)-Lipschitz on \([a,b]\), then NEWLINE\[NEWLINE|I_f(a, b)- I_f(c, d)|\leq M\cdot A(a,b,c,d),NEWLINE\]NEWLINE where \(I_f(a, b)\) is the integral mean of \(f\) on \([a, b]\), and \(A(a,b,c,d)= ((c- a)^2+ (b- d)^2)/[2(c- a+ b-d)]\).
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