Generalizations of Crooks and Lin’s results on Jeffreys–Csiszár and Jensen–Csiszár ff-divergences

•We introduce and investigate new Jeffreys–Csiszár and Jensen–Csiszár ff-divergences.•We derive inequalities for such general divergences.•We refine results by Crooks, Lin and Popescu et al. on Jeffreys and Jensen–Shannon divergences.

In this paper, Jeffreys–Csiszár and Jensen–Csiszár ff-divergences are introduced and studied. Some bounds of Crooks and Lin types for such divergences are provided. To this end the concavity of the composition of monotone functions is discussed. Refinements of the original inequalities by Crooks and Popescu et al. are given.