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

Janusz Brzdęk

ArticleOriginal scientific text

Title

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

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Affiliations

Institute of Mathematics, Pedagogical University of Rzeszów, Rejtana 16a, 35-310 Rzeszów, Poland

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)}^{n} y) = f (x) f (y)

, then it is continuous or the set {x ∈ X : f(x) ≠ 0} is a Christensen zero set.

Keywords

ENG

Gołąb-Schinzel functional equation, Christensen measurability, F-space

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Title

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

Affiliations

Abstract

Keywords

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