The stability of the entropy of degree alpha

In this paper, we first prove that the generalized fundamental equation of information depending on a positive real parameter α, is stable in the sense of Hyers and Ulam provided that α = 1, then we apply this result to prove the stability of a system of functional equations that characterizes the entropy of degree alpha or Havrda–Charvát entropy which has recently often been called the Tsallis entropy.