In this article, we introduce the multi-$m$-Jensen mappings and characterize them as a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability for such mappings. As a consequence, we show that every multi-$m$-Jensen mappings (under some conditions) is hyperstable.

Using fixed point methods, we prove the generalized Hyers–Ulam–Rassias stability of ternary homomorphisms, and ternary multipliers in ternary Banach algebras for the Jensen–type functional equation f( x+ y + z 3 ) + f( x− 2y + z 3 ) + f( x+ y − 2z 3 ) = f(x) .

In this paper, we establish the stability and superstability of J∗−derivations in J∗−algebras for the generalized Jensen–type functional equation rf( x+ y r ) + rf( x− y r ) = 2f(x). Finally, we investigate the stability of J∗−derivations by using the fixed point alternative.

where f , g are two unknown functions to be determined. Equation (A f g), raised by Wilson, is called the Wilson equation sometimes, and (Ag f ) is raised by Kannappan and Kim [9]. Let g(x) ≡ k in (Ag f ). Then we have f (x + y) + f (x − y) = 2k f (y) for all x, y ∈ G. Putting y = 0 in this equation we have f (x)= k f (0). Hence f is a constant function. Let g(y)≡ 1 in (A f g). Then we have the...