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An inconsistency equation involving means

Roman Ger, Tomasz Kochanek (2009)

Colloquium Mathematicae

We show that any quasi-arithmetic mean A φ and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations f ( M ( x , y ) ) = A φ ( f ( x ) , f ( y ) ) and f ( A φ ( x , y ) ) = M ( f ( x ) , f ( y ) ) are the constant ones.

An inequality for the coefficients of a cosine polynomial

Horst Alzer (1995)

Commentationes Mathematicae Universitatis Carolinae

We prove: If 1 2 + k = 1 n a k ( n ) cos ( k x ) 0 for all x [ 0 , 2 π ) , then 1 - a k ( n ) 1 2 k 2 n 2 for k = 1 , , n . The constant 1 / 2 is the best possible.

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