A completeness criterion for Kaniadakis, Abe and two-parameter generalized statistical theories

We recently provided a criterion of completeness valid for any generalized thermostatistics to check whether they form a bijection from ℝ+/ℝ (set of positive real numbers/all real numbers) to ℝ/ℝ+ in a previous paper. In the current work, we apply this criterion to Kaniadakis, Abe and two-parameter generalized functions and obtain their respective validity ranges.