Abstract Extension for Jensen-type inequality and reverse of Jensen’s inequality under the assumption of second-order differential inequality p (x) f (x) + q (x) f ′ (x) + f ′ ′ (x) ≥ 0 equation*p (x) f (x) +q (x) f^ (x) +f^ (x) 0 equation* are established, Hermite–Hadamard-type inequality is also proven. We get some refinements of power mean inequality as applications and further extend normalised Jensen functional under the assumption of second-order differential inequality as an improvement.
Miao et al. (Mon,) studied this question.
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