Hermite-Hadamard Type Inequalities for Interval (h1, h2)-Convex Functions

Abstract

We introduce the concept of interval ( h 1 , h 2 ) -convex functions. Under the new concept, we establish some new interval Hermite-Hadamard type inequalities, which generalize those in the literature. Also, we give some interesting examples.

New Hermite–Hadamard-type inequalities for "Equation missing"-convex fuzzy-interval-valued functions

“…Inspired by the above literature, in 2018, Zhao et al introduced h-convex interval-valued functions and proved the Hermite-Hadamard-type inequality for h-convex interval-valued functions [34]. As a step forward, An et al [2] presented the class of (h 1 , h 2 )-convex interval-valued functions and established the following interval-valued Hermite-Hadamard-type inequality for such functions:…”

Some fractional Hermite–Hadamard-type inequalities for interval-valued coordinated functions

“…where f : I → R is a convex function on the closed bounded interval I of R, and o, ς ∈ I with o < ς . Since they play a crucial role in convex analysis and can be a very powerful tool for measuring and computing errors, many authors have devoted their efforts to generalize inequalities (1.1); see [1][2][3][4][5][6]. It is worth noting that Sarikaya et al [7] established new Hermite-Hadamard-type inequalities via the Riemann-Liouville fractional integrals.…”

Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions

“…On the other hand, interval analysis was initially developed as an attempt to deal with interval uncertainty that appears in computer graphics [9], automatic error analysis [10], and many others. Recently, several authors have extended their research by combining integral inequalities with interval-valued functions (IVFs), one can see Chalco-Cano et al [11], Román-Flores et al [12], Flores-Franulič et al [13], Zhao et al [14,15], An et al [16]. As a further extension, more and more Hermite-Hadamard type inequalities involving interval Riemann-Liouville type fractional integral have been obtained for different classes of IVFs, see for interval convex functions [17], for interval harmonically convex functions [18] and the references therein.…”