An alternative equation for generalized polynomials of degree two
Abstract
In this paper we consider a generalized polynomial f : ℝ → ℝ of degree two that satisfies the additional equation f(x)f(y) = 0 for the pairs (x,y) ∈ D, where D ⊆ ℝ2 is given by some algebraic condition. In the particular cases when there exists a positive rational m fulfilling
D = { (x,y) ∈ ℝ2 | x2 - my2 = 1 },
we prove that f(x) = 0 for all x ∈ ℝ.
Keywords
additive functions; quadratic functions; generalized polynomials; alternative equation
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Institute of Mathematics, University of Debrecen Hungary
http://orcid.org/0000-0003-2219-6027
Institute of Mathematics, University of Debrecen Algeria
https://orcid.org/0000-0002-6540-8651
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