Ferreri Hypoentropy. Sharma Mital entropy as biparametric extension of Renyi. Arimoto entropy. Some are particular cases of quasilinear entropies.
Helpful:
S. Furuichi, F.-C. Mitroi, E. Symeonidis, On Some Properties of Tsallis Hypoentropies and Hypodivergences, Entropy, 16(10) (2014), 5377-5399; DOI:10.3390/e16105377; ISSN: 1099-4300
S. Furuichi, F.-C. Mitroi, Mathematical inequalities for some divergences, Physica A 391 (2012), pp.388--400, DOI:10.1016/j.physa.2011.07.052; ISSN: 0378-4371