Stability of the Fréchet Equation in Quasi-Banach Spaces

Abstract

We investigate the Hyers–Ulam stability of the well-known Fréchet functional equation that comes from a characterization of inner product spaces. We also show its hyperstability on a restricted domain. We work in the framework of quasi-Banach spaces. In the proof, a fixed point theorem due to Dung and Hang, which is an extension of a fixed point theorem in Banach spaces, plays a main role.

Keywords

• Hyers–Ulam stability
• hyperstability
• Fréchet equation
• quasi-Banach space
• fixed point theorem