Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we adopt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of a functional equation of the square root spiral, f (√ r2 + 1 ) = f(r)+ tan−1(1/r).

In this paper, we give some properties of the bi-Jensen functional equation and investigate its Hyers–Ulam stability hyperstability. We construct a function which is not continuous. Additionally, on restricted unbounded domains. Finally, apply obtained results to study interesting asymptotic behaviors functions.