Two fixed functions can approximate any continuous function using only addition and composition
Functional Analysis
2026-05-27 v1
Abstract
We prove that two fixed univariate functions, namely, an arbitrary continuous non-affine function and a concrete affine function, are sufficient to approximate continuous functions of one variable under the operations of addition and composition. The same fixed functions can also be used to approximate multivariate continuous functions, provided that the coordinate functions are also available.
Cite
@article{arxiv.2605.26550,
title = {Two fixed functions can approximate any continuous function using only addition and composition},
author = {Vugar Ismailov},
journal= {arXiv preprint arXiv:2605.26550},
year = {2026}
}
Comments
17 pages, 19 references; this paper extends and strengthens some material that appeared in arXiv:2604.23765v2