Articles written in Proceedings – Mathematical Sciences
Volume 124 Issue 3 August 2014 pp 365-381
In this paper, we study the Hyers–Ulam stability of a simple Levi–Civitá functional equation $f(x+y)=f(x)h(y)+f(y)$ and its pexiderization $f(x+y)=g(x) h(y)+k(y)$ on non-unital commutative semigroups by investigating the functional inequalities $|f(x+y)-f (x)h(y)-f(y)|\leq \epsilon$ and $|f(x+y)-g(x)h(y)-k(y)|\leq \epsilon$, respectively. We also study the bounded solutions of the simple Levi–Civitá functional inequality.
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