2013/07/16 by Eszter Gselmann, Gselmann, Eszter
Mathematics · #39B72 #39B82 #Advanced Topics in Algebra #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical and Theoretical Analysis #math.CA #msc:39B72 #msc:39B82
paper · pdf · doi:10.48550/arxiv.1307.4277
9 pages
arxiv created 2013/07/16 · openalex publication_date 2013/07/16 · arxiv updated 2013/07/17 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
The main aim of this note is to provide characterization theorems concerning real derivations. Among others the following implication will be verified: Assume that ξ\colon ℝ→ ℝ is a given differentiable function and for the additive function d\colon ℝ→ ℝ, the mapping x\longmapsto d(ξ(x))-ξ'(x)d(x) is regular (e. g. measurable, continuous, locally bounded). Then d is a sum of a derivation and a linear function.