On the stability of the quadratic mapping in normed spaces

Abstract

The Hyers-Ulam stability, the Hyers-Ulam-Rassias stability, and also the stability in the spirit of Gavruţa for each of the following quadratic functional equationsf(x+y)+f(x−y)=2f(x)+2f(y),f(x+y+z)+f(x−y)+f(y−z)+f(z−x)=3f(x)+3f(y)+3f(z),f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(z+x)are investigated.