Sections in functional equations: stability and hyperstability

General hyperstability criteria for Jensen-type equations

“…We give here a couple of hyperstability results for some equations whose solutions are composite functions of the form ρ • g, where ρ : X → Y is a Jensen function on D. For this we adopt a very simplified form of the section method described in [5] and [6].…”

“…Joung [8] proves the Ulam stability of the Jensen equation on a restricted domain and uses it to characterize the additivity of the mappings. Solving techniques for a functional equation with composite solutions using its characteristic equation (the so-called section method) -have been described in [5]; several cases in which the stability or hyperstability of the characteristic equation is transmitted to the original equation are analyzed in [6]. A study similar to the present one, but made for Cauchy-type equations, was carried out in [7].…”