A simple proof and extensions of an inequality (Q1977790)
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scientific article; zbMATH DE number 1449178
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple proof and extensions of an inequality |
scientific article; zbMATH DE number 1449178 |
Statements
A simple proof and extensions of an inequality (English)
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23 September 2001
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New proofs of the following two inequalities are offered: \[ (b^{x+ y}- a^{x+y})/(b^x- a^x)\geq (x+ y)[(a+ b)/2]/x,\quad\text{where }0< a< b,\quad 1\leq x,y \] and \[ (b^{x+ y}- a^{x+ y})/(b^x- a^x)\geq (x+ y)[(ab)^{y/2}]/x,\quad\text{where }0< a< b,\quad 0< x,y. \] The proofs use the monotonicity of the Stolarsky means \(E(r,s,a,b)\).
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inequalities
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monotonicity
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Stolarsky means
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0.8216577768325806
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0.8035354614257812
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