Stability and hyperstability of a quadratic functional equation and a characterization of inner product spaces

Abstract

We have proved theHyers-Ulam stability and the hyperstability of the quadratic functional equation f (x + y + z) + f (x + y − z) + f (x − y + z) + f (−x + y + z) = 4[f (x) + f (y) + f (z)] in the class of functions from an abelian group G into a Banach space.

Keywords

• Hyers-Ulam stability
• hyperstability
• quadratic functional equation
• fixed point theorem
• 39B82
• 39B52
• 47H14
• 47H10