The main purpose of the presented paper is to obtain some time scale inequalities for different divergences and distances by using weighted time scales Jensen’s inequality. These results offer new inequalities in h-discrete calculus and quantum calculus and extend some known results in the literature. The lower bounds of some divergence measures are also presented. Moreover, the obtained discrete results are given in the light of the Zipf–Mandelbrot law and the Zipf law.

中文翻译：

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通过时间尺度上的加权 Jensen 不等式估计发散度量

本文的主要目的是通过使用加权时间尺度 Jensen 不等式来获得不同散度和距离的一些时间尺度不等式。这些结果在 h 离散微积分和量子微积分中提供了新的不等式，并扩展了文献中的一些已知结果。还提供了一些分歧度量的下限。此外，获得的离散结果是根据 Zipf-Mandelbrot 定律和 Zipf 定律给出的。