Stability of a generalization of the Fréchet functional equation

Abstract

We prove some stability and hyperstability results for a generalization of the well known Fréchet functional equation, stemming from one of the characterizations of the inner product spaces. As the main tool we use a fixed point theorem for the function spaces. We end the paper with some new inequalities characterizing the inner product spaces.

Keywords

• stability
• hyperstability
• characterization of inner product spaces
• fixed point theorem
• Fréchet equation