Levinson type inequalities are generalized by using Hermite interpolating polynomial for the class of $\mathfrak{n}$-convex functions. In seek of application to information theory, some estimates for new functional are obtained based on f divergence. Inequalities involving Shannon entropies are also discussed.

中文翻译：

---

通过Hermite插值多项式对高阶凸函数使用Levinson型不等式估计f-散度和Shannon熵

通过使用Hermite插值多项式对$ \ mathfrak {n} $-凸函数类推广Levinson型不等式。为了将其应用到信息论中，基于f散度获得了一些新功能的估计。还讨论了涉及香农熵的不等式。