Approximate pexiderized Cauchy's additive type mappings

Abstract

We prove the stability of the Pexiderized Cauchy's additive functional equation with a general form; f(x+y )= g(x)+h(y)+λ(x,y) where λ(x,y) is a logarithm of a pseudo exponential function. From this result, we obtain the stability with the following form; 1 1+ φ(x,y) f(x+y) e(x,y)g(x)h(y) 1+ φ(x,y), where e(x,y) is a pseudo exponential function. It is a generalized result for the stability of the Pexiderized Cauchy's functional equation.