Abstract
The Hermite–Hadamard inequality was extended using iterated integrals by Retkes [Acta Sci Math (Szeged) 74:95–106, 2008]. In this paper we further extend the main results of the above paper for convex and also for s-convex functions in the second sense.
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Breckner, W.W.: Stetigkeitsaussagen für eine Klasse verallgemeinerter Konvexer funktionen in topologischen linearen Räumen. Publ. Inst. Math. 23, 13–20 (1978)
Chen, X.: New convex functions in linear spaces and Jensen’s discrete inequality. J. Inequal. Appl. 2013, 472 (2013)
Dragomir, S.S., Fitzpatrick, S.: The Hadamard’s inequality for \(s\)-convex functions in the second sense. Demonstr. Math. 32(4), 687–696 (1999)
Hudzik, H., Maligranda, L.: Some remarks on \(s\)-convex functions. Aequat. Math. 48, 100–111 (1994)
Özdemir, M.E., Yıldız, Ç., Akdemir, A.O., Set, E.: On some inequalities for \(s\)-convex functions and applications. J. Inequal. Appl. 2013, 333 (2013)
Retkes, Z.: An extension of the Hermite–Hadamard inequality. Acta Sci. Math. (Szeged) 74, 95–106 (2008)
Retkes, Z.: Applications of the extended Hermite–Hadamard inequality. J Inequal. Pure Appl. Math. (JIPAM) 7 (1) (2006), article 24
Xi, B.-Y., Qi, F.: Inequalities of Hermite–Hadamard type for extended \(s\)-convex functions and applications to means. J. Nonlinear Convex Anal. 16(5), 873–890 (2015)
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Kórus, P. An extension of the Hermite–Hadamard inequality for convex and s-convex functions. Aequat. Math. 93, 527–534 (2019). https://doi.org/10.1007/s00010-019-00642-z
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DOI: https://doi.org/10.1007/s00010-019-00642-z