This paper investigates the dualities of two-parameter entropies, Sk,r Kaniadakis et al. (2005). Two kinds of dualities are found, namely inverse (r→−r) and inverse-scaling (r→−rs,k→ks) which recovers the additive (q→2−q) and multiplicative (q→1/q) dualities in the Tsallis limit.

In this paper, by considering the first three Khinchin axioms (K1–K3) and neglecting the fourth (K4), a set of new three-parameter entropies will be introduced which are expressed in terms of a generalized incomplete Gamma function as Sd,c1,c2[p]∝∑iΓ(d+1,1−c1lnpi,1−c2lnpi). Also, its...