Separation via quadratic functions. (Summary).
Sesquilinear-orthogonally quadratic mappings.
Small sets and a class of general functions.
Smoothness in disjoint groups of real functions under composition.
Sobre algunas medias de funciones asociativas.
Some functional equations involving means of associative functions are investigated.
Sobre la sección diagonal y la región cero de una t-norma.
We prove that two archimedean t-norms with equal diagonal sections and zero-sets must be identical.
Solution and stability of a mixed type additive, quadratic, and cubic functional equation.
Solution and stability of a mixed type cubic and quartic functional equation in quasi-Banach spaces.
Solution complète au problème de Siegel de linéarisation d'une application holomorphe au voisinage d'un point fixe
Solution générale d'une classe d'équations fonctionnelles cycliques linéaires et non homogènes
Solution générale d'une classe des équations fonctionnelles cycliques linéaires et homogènes
Solution générale d'une équation fonctionelle dans le domaine des fonctions analytiques
Solution générale sur un groupe abélien de l'équation fonctionelle f(x*f(y)) = f(f(x)*y).
Solution of (2, 2)-type sum form functional equations with several unknown functions.
Solution of a Cauchy-Jensen stability Ulam type problem
In 1978 P. M. Gruber (Trans. Amer. Math. Soc. 245 (1978), 263–277) imposed the following general problem or Ulam type problem: “Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate this objects by objects, satisfying the property exactly?" The afore-mentioned problem of P. M. Gruber is more general than the following problem imposed by S. M. Ulam in 1940 (Intersci, Publ., Inc., New York 1960): “Give conditions in order for a linear mapping...
Solution of a quadratic stability Ulam type problem
In 1940 S. M. Ulam (Intersci. Publ., Inc., New York 1960) imposed at the University of Wisconsin the problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist”. According to P. M. Gruber (Trans. Amer. Math. Soc. 245 (1978), 263–277) the afore-mentioned problem of S. M. Ulam belongs to the following general problem or Ulam type problem: “Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate this objects...
Solution of a sum form equation in the two dimensional closed domain case.
Solution of Cauchy's functional equation on a restricted domain
Solution of distributive-like quasigroup functional equations
We are investigating quasigroup functional equation classification up to parastrophic equivalence [Sokhatsky F.M.: On classification of functional equations on quasigroups, Ukrainian Math. J. 56 (2004), no. 4, 1259–1266 (in Ukrainian)]. If functional equations are parastrophically equivalent, then their functional variables can be renamed in such a way that the obtained equations are equivalent, i.e., their solution sets are equal. There exist five classes of generalized distributive-like quasigroup...
Solution of nonlinear functional equations in linear normed spaces