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Abstract Pythagorean theorem and corresponding functional equations

In: Tatra Mountains Mathematical Publications, vol. 55, no. 2
Roman Ger
Detaily:
Rok, strany: 2013, 67 - 75
Kľúčové slová:
Pythagorean theorem, height function, associativity, quasi-arithmetic mean
O článku:
Motivated by a result of [Lucio R. Berrone: The associativity of the Pythagorean law, Amer. Math. Monthly 116 (2009), 936–939] we deal with the functional equation

$$ f(x+y) = f(x) + f(y) + 2 f(Φ(x,y)) $$

and its variants to distinguish the classical Pythagorean theorem from among its numerous abstract generalizations.
Ako citovať:
ISO 690:
Ger, R. 2013. Abstract Pythagorean theorem and corresponding functional equations. In Tatra Mountains Mathematical Publications, vol. 55, no.2, pp. 67-75. 1210-3195.

APA:
Ger, R. (2013). Abstract Pythagorean theorem and corresponding functional equations. Tatra Mountains Mathematical Publications, 55(2), 67-75. 1210-3195.