Approximate gamma–beta type functions Original Research Article

We show that every unbounded approximate gamma–beta type function is of gamma–beta type. That is, we obtain the superstability of a gamma–beta type functional equation β(x,y)f(x+y)=f(x)f(y)β(x,y)f(x+y)=f(x)f(y) Turn MathJax on and also investigate the stability in the sense of RR. Ger of this equation in the following setting : View the MathML source|β(x,y)f(x+y)f(x)f(y)−1|≤φ(x,y). Turn MathJax on From these results, we obtain stabilities of a generalized exponential functional equation and Cauchy’s gamma–beta functional equation.