In this paper, we investigate the generalized Hyers-Ulam stability of the functional inequality $$||af(x)+bf(y)+cf(z)||{\leq}||f(ax+by+cz))||+{\phi}(x,y,z)$$ associated with Cauchy additive mappings. As a result, we obtain that if a mapping satisfies ...
In this paper, we investigate the generalized Hyers-Ulam stability of the functional inequality $$||af(x)+bf(y)+cf(z)||{\leq}||f(ax+by+cz))||+{\phi}(x,y,z)$$ associated with Cauchy additive mappings. As a result, we obtain that if a mapping satisfies the functional inequality with perturbing term which satisfies certain conditions then there exists a Cauchy additive mapping near the mapping.