Fractional Hermite–Hadamard type inequalities for interval-valued functions

Abstract

We introduce the concept of interval harmonically convex functions. By using two different classes of convexity, we get some further refinements for interval fractional Hermite-Hadamard type inequalities. Also, some examples are presented. MSC: 26D15; 26E25; 26A33

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

“…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.…”

Weighted Hermite–Hadamard type inclusions for products of co-ordinated convex interval-valued functions

“…In addition, some inclusions involving interval-valued Riemann-Liouville fractional integrals have been derived by Budak et al in [7]. In [28], Liu et al gave the definition of interval-valued harmonically convex functions, and so they have some Hermite-Hadamard type inclusions including interval fractional integrals. For more details about this topic, you can look over the references [13, 14, 32, 34-36, 45, 55, 56].…”

“…[28]) Suppose that w : [ , ς] → R is nonnegative, integrable, and symmetric about ξ = +ς 2 (i.e. w(ξ ) = w( + ςξ )).…”

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

“…Mohammed and Abdeljawad [9] proved new Hermite-Hadamard-type inequalities in the context of fractional calculus with respect to functions involving nonsingular kernels. For other related results, we refer the readers to [7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…Román-Flores et al [24] derived the Minkowski and Beckenbach-type inequalities for interval-valued functions. Liu et al [18] proved Hermite-Hadamard-type inequalities via interval Riemann-Liouville-type fractional integrals for interval-valued functions. Very recently, Zhao et al [25,26] established Hermite-Hadamard-type inequalities for interval-valued coordinated functions.…”