Abstract In this paper we give some hyperstability and stability results for the Cauchy Jensen functional equations on restricted domains. We provide a simple short proof Brzde?k’s result concerning equation.

Symmetry is repetitive self-similarity. We proved the stability problem by replicating well-known Cauchy equation and Jensen into two variables. In this paper, we Hyers-Ulam of bi-additive functional f(x+y,z+w)=f(x,z)+f(y,w) bi-Jensen 4fx+y2,z+w2=f(x,z)+f(x,w)+f(y,z)+f(y,w).

‎The aim of this paper is to introduce and solve the‎ radical cubic functional equation‎ ‎$‎‎fleft(sqrt[3]{x^{3}+y^{3}}right)+fleft(sqrt[3]{x^{3}-y^{3}}right)=2f(x)‎$.‎ ‎We also investigate some stability and hyperstability results for‎ ‎the considered equation in 2-Banach spaces‎.

In this paper, we establish the generalized Hyers–Ulam–Rassias stability of homomorphisms between ternary algebras associted to the generalized Jensen functional equation rf( sx+ty r ) = sf(x) + tf(y).

We use a fixed point method to prove the Cauchy–Rassias stability of homomorphisms associated to the Pexiderized Cauchy–Jensen type functional equation r f ( x+ y r ) + sg ( x− y s ) = 2h(x), r,s ∈ R\{0}