Stability of a Bi-Jensen Functional Equation on Restricted Unbounded Domains and Some Asymptotic Behaviors

Abstract

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

Keywords

• Hyers–Ulam stability
• functional equation
• bi-Jensen function
• ε-bi-Jensen function
• asymptotic behavior