Zoltán Boros

Hyers–Ulam stability of derivations and linear functions

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.

Stability of the Multiplicative Cauchy Functional Equation in Ordered Fields

An analogue of Baker’s superstability theorem, a related example, and further stability type results concerning the multiplicative Cauchy functional equation are presented for functions with values in ordered fields.

Note on Multilinear Functions and Algebraic Dependence

The construction of a specific multiadditive function leads to a structure theorem on the set of vectors with algebraically dependent components. A counterexample in the theory of quadratic functions is also obtained.