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In the article, we establish several Petrović-type inequalities for the harmonic h -convex (concave) function if h is a submultiplicative (super-multiplicative) function, provide some new majorizaton type inequalities for harmonic convex function, and prove the superadditivity, subadditivity, linearity, and monotonicity properties for the functionals derived from the Petrović type inequalities.
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Baloch et al. (2020) studied this question.
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