On a variant of Čebyšev’s inequality of the Mercer type

Abstract

Abstract 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.

Keywords

• Jensen–Mercer inequality
• Čebyšev’s inequality of the Mercer type