Hermite–Hadamard-type inequalities for the interval-valued approximately h -convex functions via generalized fractional integrals

[摘要] In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

[学科分类] 电力

[关键词] Hermite–Hadamard-type inequalities;Interval-valued functions;Fractional integrals