Stability (learning theory)

Normed vector space

Pure mathematics

Symmetry (geometry)

Mathematics

Evolutionary biology

Biology

Partial differential equation

Epistemology

Machine learning

Functional equation

Mathematical analysis

Philosophy

Function (biology)

Geometry

Computer science

Simple (philosophy)

Point (geometry)

Applied mathematics

Symmetry

Ulam stability is motivated by the following issue: how much an approximate solution of an equation differs from the exact solutions to the equation. It is connected to some other areas of investigation, e.g., optimization, approximation theory and shadowing. In this paper, we present and discuss the published results on such stability for functional equations in the classes of function-taking values in 2-normed spaces. In particular, we point to several pitfalls they contain and provide possible simple improvements to some of them. Thus we show that the easily noticeable symmetry between them and the analogous results proven for normed spaces is, in fact, mainly apparent. Our article complements the earlier similar review published in Symmetry (13(11), 2200) because it concerns the outcomes that have not been discussed in this earlier publication.

On Ulam Stability of Functional Equations in 2-Normed Spaces—A Survey II