We consider the discrete Jensen–Mercer inequality and Čebyšev’s inequality of the Mercer type. We establish bounds for Čebyšev’s functional of the Mercer type and bounds for the Jensen–Mercer functional in terms of the discrete Ostrowski inequality. Consequentially, we obtain new refinements of the considered inequalities.

中文翻译：

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关于ČebyševMercer型不等式的一个变体

我们考虑了离散的Jensen-Mercer不等式和Čerbyšev的Mercer型不等式。根据离散的Ostrowski不等式，我们确定了Čerbyšev函数的Mercer类型的界限，以及Jensen–Mercer函数的界限。因此，我们对考虑的不平等现象进行了新的完善。