Operatorial approach to the non-Archimedean stability of a Pexider K-quadratic functional equation

Abstract

We use the operatorial approach to obtain, in non-Archimedean spaces, the Hyers–Ulam stability of the Pexider K-quadratic functional equation∑k∈Kf(x+k·y)=κg(x)+κh(y),x,y∈E, where f,g,h:E→F are applications and K is a finite subgroup of the group of automorphisms of E and κ is its order.

Keywords

• Group automorphisms
• Jensen functional equation
• Quadratic functional equation
• K-quadratic functional equation
• Pexider functional equation
• Non-Archimedean Hyers–Ulam stability