Random stability of an additive-quadratic-quartic functional equation.
Recent results on the stability of the parametric fundamental equation of information.
Remarks on orthogonality preserving mappings in normed spaces and some stability problems.
Separation of convex polyhedral sets with column parameters
Separation is a famous principle and separation properties are important for optimization theory and various applications. In practice, input data are rarely known exactly and it is advisable to deal with parameters. In this article, we are concerned with the basic characteristics (existence, description, stability etc.) of separating hyperplanes of two convex polyhedral sets depending on parameters. We study the case, when parameters are situated in one column of the constraint matrix from the...
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 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...
Solutions and stability of generalized mixed type QC functional equations in random normed spaces.
Some remarks on stability and solvability of linear functional equations.
Some remarks on the stability of the multi-Jensen equation
First a stability result of Prager-Schwaiger [Prager W., Schwaiger J., Stability of the multi-Jensen equation, Bull. Korean Math. Soc., 2008, 45(1), 133–142] is generalized by admitting more general domains of the involved function and by allowing the bound to be not constant. Next a result by Cieplinski [Cieplinski K., On multi-Jensen functions and Jensen difference, Bull. Korean Math. Soc., 2008, 45(4), 729–737] is discussed. Finally a characterization of the completeness of a normed space in...
Stability and superstability of ring homomorphisms on non-archimedean Banach algebras.
Stability aspects of arithmetic functions
Stability aspects of arithmetic functions, II
Stability of a 2-dimensional functional equation in a class of vector variable functions.
Stability of a bi-Jensen functional equation. II.
Stability of a Cauchy-Jensen functional equation in quasi-Banach spaces.
Stability of a functional equation coming from the characterization of the absolute value of additive functions.
Stability of a functional equation deriving from cubic and quartic functions.
Stability of a functional equation related to distance measure. II.
Stability of a generalization of the Fréchet functional equation
We prove some stability and hyperstability results for a generalization of the well known Fréchet functional equation, stemming from one of the characterizations of the inner product spaces. As the main tool we use a fixed point theorem for some function spaces. We end the paper with some new inequalities characterizing the inner product spaces.