Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals
Dafang Zhao, Muhammad Aamir Ali, Artion Kashuri, Hüseyin Budak, Mehmet Zeki Sarıkaya
Abstract
Abstract 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.
Topics & Concepts
MathematicsHermite polynomialsConvex functionHadamard transformInterval (graph theory)Type (biology)Regular polygonPure mathematicsFunction (biology)Class (philosophy)CombinatoricsMathematical analysisBiologyGeometryComputer scienceEcologyEvolutionary biologyArtificial intelligenceMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsApproximation Theory and Sequence Spaces