New Jensen and Hermite–Hadamard type inequalities for h-convex interval-valued functions

Abstract

In this paper, we introduce the h-convex concept for interval-valued functions. By using the h-convex concept, we present new Jensen and Hermite-Hadamard type inequalities for interval-valued functions. Our inequalities generalize some known results.

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

“…Recently, some of these inequalities have been extended to interval-valued functions by Chalco-Cano et al; see, e.g., [10][11][12][13][14][15][16]. Surprisingly enough, interval Hermite-Hadamard type inequalities has perhaps not received enough attention [17]. For convenience, we recall the classical Hermite-Hadamard inequality.…”

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

“…If h(ν) = ν, then we get Theorem 3.5 of [17]. If α = 1, then we get Theorem 4.5 of [14]. If f = f and α = 1, then we get Theorem 7 of [4].…”

“…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.…”

Fractional Hermite–Hadamard type inequalities for interval-valued functions

“…For more basic notations with interval analysis, see [24,25]. Furthermore, we recall the following results in [20].…”

“…Especially, several classical inequalities have been studied with interval-valued functions by Chalco-Cano et al [21,22], Costa and Román-Flores. [23], Zhao et al [24,25], An et al [26], and so on. As a further extension, Budak et al [27] proved the fractional Hermite-Hadamard inequality for interval convex function.…”