A general reverse Pinsker's inequality is derived to give an upper bound on f-divergences in terms of total variational distance when two distributions are close measured under our proposed generalized local information geometry framework. In addition, relationships between two f-divergences equipped with functions that are third order differentiable are established in terms of the lower and upper bounds of their ratio, when the underlying distributions are within a generalized quasi-$\varepsilon$-neighborhood.

翻译：在提出的广义局部信息几何框架下，当两个分布接近时，我们推导了一个广义逆Pinsker不等式，以全变差距离给出f-散度的上界。此外，当基础分布位于广义拟-$\varepsilon$-邻域内时，我们建立了两个具有三阶可导函数的f-散度之间关系的下界和上界比。