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Superstability of the Cauchy equation with squares in finite-dimensional normed algebras

Authors:	Bogdan?Batko author-information" > author-information__contact u-icon-before" > mailto:bbatko@up.krakow.pl" title=" bbatko@up.krakow.pl" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	1.Institute of Mathematics,Pedagogical University of Cracow,Kraków,Poland;2.Department of Computational Mathematics,WSB-NLU,Nowy Sa?cz,Poland

Abstract:	Our purpose is to provide an affirmative answer to Moszner’s problem [cf. Moszner (Ann Univ Paed Crac Stud Math XI:69–94, 2012), p. 93] concerning the superstability of the Cauchy equation with squares $$f(x + y)^2 = (f(x) + f(y))^2$$ in the class of functions mapping an Abelian semigroup into a finite-dimensional normed algebra without divisors of zero.

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