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

Volume 64 / 1996

Janusz Brzdęk Annales Polonici Mathematici 64 (1996), 195-205 DOI: 10.4064/ap-64-3-195-205

Abstract

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.

Authors

  • Janusz Brzdęk

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