A conditional equation for additive functions

• Autores: Zoltán Boros, Péter Erdei
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 70, Nº. 3, 2005, págs. 309-313
• Idioma: inglés
• DOI: 10.1007/s00010-005-2810-x
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• Resumen

  • Let S denote the set of all pairs (x, y) of real numbers that satisfy the condition x2 + y2 = 1. It was asked by Walter Benz in 1988 whether an additive real function f that fulfils the equation x f (x) + y f (y) = 0 or y f (x) = x f (y) for every (x, y) S must be a derivation or a linear function, respectively. Both questions are answered in the affirmative.