Some integral inequalities for interval-valued functions

On Hermite-Hadamard type inequalities for harmonical h-convex interval-valued functions

“…In [3,4], Chalco-Cano et al obtained Ostrowski type inequalities for interval-valued functions by using Hukuhara derivative for interval-valued functions. In [18], Román-Flores et al established Minkowski and Beckenbach's inequalities for intervalvalued functions. For the others, please see [5,6,9,18,19].…”

“…In [18], Román-Flores et al established Minkowski and Beckenbach's inequalities for intervalvalued functions. For the others, please see [5,6,9,18,19]. However, inequalities were studied for more general set-valued maps.…”

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

“…Among the many types of inequalities, those carrying the names of Jensen, Hermite-Hadamard, Hardy, Ostrowski, Minkowski and Opial et al have a deep significance and have made a great impact in substantial fields of research. 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].…”

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.…”