The proposed two-parameter entropy reduces, by the paper's own formulas, to the one-parameter Tsallis entropy S_q with q=2k+1, independent of r.
Information theoretical properties of tsallis e ntropies
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A two-parameter entropy and its fundamental properties
The proposed two-parameter entropy reduces, by the paper's own formulas, to the one-parameter Tsallis entropy S_q with q=2k+1, independent of r.