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The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation

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Brzdęk J.

Annales Polonici Mathematici

1996

tom 64

nr 3

195-205

Let K denote the set of all reals or complex numbers. Let X be a topological linear separable F-space over K. The following generalization of the result of C. G. Popa [16] is proved. Theorem. Let n be a positive integer. If a Christensen measurable function f: X → K satisfies the functional equation $f(x + f(x)^ny) = f(x)f(y)$, then it is continuous or the set {x ∈ X : f(x) ≠ 0} is a Christensen zero set.

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1 Annales Polonici Mathematici

1 Brzdęk J.

1 1996

Wyniki wyszukiwania

The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation