On superstability of exponential functional equations

Abstract

Abstract The aim of this paper is to prove the superstability of the following functional equations: f ( P ( x , y ) ) = g ( x ) h ( y ) , f ( x + y ) = g ( x ) h ( y ) . $$\begin{aligned}& f \bigl(P(x,y) \bigr)= g(x)h(y), \\& f(x+y)=g(x)h(y). \end{aligned}$$

Keywords

• Banach algebra
• Pexider exponential equation
• Exponential function
• Superstability