A note on the definition of deformed exponential and logarithm functions

摘要: The recent generalizations of the Boltzmann–Gibbs statistics mathematically rely on deformed logarithmic and exponential functions defined through some deformation parameters. In present work, we investigate whether a logarithmic/exponential map is bijection from R+/R (set positive real numbers/all numbers) to R/R+, as their undeformed counterparts. We show that inverse exists only in subsets aforementioned (co)domains. Furthermore, conditions which generalized function has satisfy, so most important properties ordinary are preserved. fulfillment these permits us determine validity interval finally apply our analysis Tsallis q-deformed discuss concavity Renyi entropy.