Abstract. We deal with the stability question for multiplicative mappings in the sense of number theory. It turns out that the conditional stability assumption:implies that f lies near to some number-theoretically multiplicative function. The domain of f can be general enough to admit, in special cases, the reduction of our result to the well known J. A. Baker -J. Lawrence -F. Zorzitto superstability theorem.
We establish a theorem of the type "measurability implies continuity" for solutions f of the functional equationunder reasonable conditions upon the integers αi, βi and the mappings Γ, Φ.
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