Approximately additive Schwartz distributions
A distributional analogue of the Rassias inequality \(\| f(x+y)-f(x)-f(y)\| \leq \varepsilon(\| x\| ^p+\| y\| ^p)\) was investigated for \(p=4, 6, 8, \dots\) by \textit{J. Chung} in [J. Math. Anal. Appl. 300, No. 2, 343--350 (2004; Zbl 1066.39028)]. In this paper, the author generalizes his previous stability result to all \(p \geq 0, p \neq 1\), and in fact for a certain general control function \(\psi(x, y)\) instead of \(\varepsilon(\| x\| ^p+\| y\| ^p)\), in the space of Schwartz (tempered) distributions.
scientific article; zbMATH DE number 5073037