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 , then it is continuous or the set x ∈ X : f(x) ≠ 0 is a Christensen zero set.
@article{bwmeta1.element.bwnjournal-article-apmv64z3p195bwm,
author = {Janusz Brzd\k ek},
title = {The Christensen measurable solutions of a generalization of the Go\l \k ab-Schinzel functional equation},
journal = {Annales Polonici Mathematici},
volume = {63},
year = {1996},
pages = {195-205},
zbl = {0860.39034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv64z3p195bwm}
}
Janusz Brzdęk. The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation. Annales Polonici Mathematici, Tome 63 (1996) pp. 195-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv64z3p195bwm/
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