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Hyers-Ulam stability of Davison functional equation on restricted domains

Park Choonkil, Tareeghee Mohammad Amin, Najati Abbas, Noori Batool

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20240039

In this article, we study the Hyers-Ulam stability of Davison functional equation f(xy)+f(x+y)=f(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), for x,y ∈ R⩾0 = {t ∈ R : t ⩾ 0}.