On generalization of some inequalities for generalized harmonically convex functions via local fractional integrals

Abstract

Based on the theory of local fractional calculus and generalized harmonically convex function on fractal sets, the author establishes a general identity involving local fractional integrals. Using this identity, some inequalities on generalization of Hermite-Hadamard, Ostrowski and Simpson type inequalities for functions whose absolute values of derivatives are generalized harmonically convex function involving local fractional integrals are obtained. Finally, some applications of these inequalities for α-type special means are given.

Key words: Hermite-Hadamard inequality, Ostrowski inequality, Simpson inequality, generalized harmonically convex function, fractal set, local fractional integral.