Abstract
Using the Ohlin lemma on convex stochastic ordering we prove inequalities of the Hermite–Hadamard type. Namely, we determine all numbers \({a,\alpha,\beta\in[0,1]}\) such that for all convex functions f the inequality
is satisfied and all \({a,b,c,\alpha\in(0,1)}\) with a + b + c = 1 for which we have
.
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Bessenyei M., Páles Zs.: Characterization of higher order monotonicity via integral inequalities. Proc. Roy. Soc. Edinb. Sect. A 140(4), 723–736 (2010)
Bullen, P.S.: Error estimates for some elementary quadrature rules. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 602–633 (1978), 97–103 (1979)
Dragomir, S.S., Pearce, C.E.M.: Selected topics on Hermite–Hadamard inequalities and applications (2000)
El Farissi A.: Simple proof and refinement of Hermite–Hadamard inequality. J. Math. Inequal. 4(3), 365–369 (2010)
Franjić, I., Pečarić, J., Perić, I., Vukelić, A.: Euler integral identity, quadrature formulae and error estimations (from the point of view of inequality theory) Monographs in Inequalities, 2. ELEMENT, Zagreb (2011)
Klaričić Bakula M., Pečarić J.: Generalized Hadamard’s inequalities based on general Euler 4-point formulae. ANZIAM J. 48, 387–404 (2007)
Ohlin J.: On a class of measures of dispersion with application to optimal reinsurance. ASTIN Bull. 5, 249–266 (1969)
Rajba T.: On The Ohlin lemma for Hermite–Hadamard–Fejer type inequalities. Math. Ineq. Appl. 17(2), 557–571 (2014)
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Szostok, T. Ohlin’s lemma and some inequalities of the Hermite–Hadamard type. Aequat. Math. 89, 915–926 (2015). https://doi.org/10.1007/s00010-014-0286-2
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DOI: https://doi.org/10.1007/s00010-014-0286-2