%0 Journal Article
%T Hyers--Ulam stability of derivations and linear functions
%A Zoltš¢n Boros
%A Eszter Gselmann
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/s00010-010-0026-1
%X In this paper the following implication is verified for certain basic algebraic curves: if the additive real function $f$ approximately (i.e., with a bounded error) satisfies the derivation rule along the graph of the algebraic curve in consideration, then $f$ can be represented as the sum of a derivation and a linear function. When, instead of the additivity of $f$, it is assumed that, in addition, the Cauchy difference of $f$ is bounded, a stability theorem is obtained for such characterizations of derivations.
%U http://arxiv.org/abs/1307.0638v1