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) 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}. Open Access.