Hyers-Ulam stability of Davison functional equation on restricted domains

Abstract

In this article, we study the Hyers-Ulam stability of Davison functional equation f(xy)+f(x+y)=f(xy+x)+f(y)f\left(xy)+f\left(x+y)=f\left(xy+x)+f(y) on some unbounded restricted domains. Using the obtained results, we study an interesting asymptotic behavior of Davison functions. We also investigate the Hyers-Ulam stability of Davison functional equation and its generalized form given by f(xy)+g(x+y)=h(xy+x)+k(y),f\left(xy)+g\left(x+y)=h\left(xy+x)+k(y), for x,y∈R⩾0={t∈R:t⩾0}x,y\in {{\mathbb{R}}}^{\geqslant 0}=\left\{t\in {\mathbb{R}}:t\geqslant 0\right\}.

Keywords

• hyers-ulam stability
• davison functional equation
• davison function
• asymptotic behavior
• 39b82
• 39b62