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On the generalized inequalities of the Hermite-Hadamard type

Nápoles Valdés Juan E. (UNNE, FaCENA, Corrientes, Argentina + UTN-FRRE, Resistencia, Chaco, Argentina), jnapoles@exa.unne.edu.ar
Bayraktar Bahtiyar (Bursa Uludag University, Faculty of Education, Gorukle Campus, Bursa, Turkey), bbayraktar@uludag.edu.tr

In this paper, we establish new Hermite-Hadamard inequalities for h-convex functions, with in the framework of a previously defined generalized integral. The results obtained, generalize or complete, several reported in the literature. Some final remarks show the strength and scope of our results.

Keywords: Generalized integral operator, Hermite-Hadamard inequality, Hölder inequality, power mean inequality, h-convex function