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

• Volume: 64, Issue: 3, page 195-205
• ISSN: 0066-2216

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## Abstract

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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 $f\left(x+f{\left(x\right)}^{n}y\right)=f\left(x\right)f\left(y\right)$, then it is continuous or the set x ∈ X : f(x) ≠ 0 is a Christensen zero set.

## How to cite

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Janusz Brzdęk. "The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation." Annales Polonici Mathematici 64.3 (1996): 195-205. <http://eudml.org/doc/269942>.

@article{JanuszBrzdęk1996,
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.},
author = {Janusz Brzdęk},
journal = {Annales Polonici Mathematici},
keywords = {Gołąb-Schinzel functional equation; Christensen measurability; F-space; Christensen measurable function; Golab-Schinzel equation; linear separable -space; Christensen zero set; continuous solutions},
language = {eng},
number = {3},
pages = {195-205},
title = {The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation},
url = {http://eudml.org/doc/269942},
volume = {64},
year = {1996},
}

TY - JOUR
AU - Janusz Brzdęk
TI - The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation
JO - Annales Polonici Mathematici
PY - 1996
VL - 64
IS - 3
SP - 195
EP - 205
AB - 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.
LA - eng
KW - Gołąb-Schinzel functional equation; Christensen measurability; F-space; Christensen measurable function; Golab-Schinzel equation; linear separable -space; Christensen zero set; continuous solutions
UR - http://eudml.org/doc/269942
ER -

## References

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