A generalization of Simpson’s inequality via differentiable mapping using extended (s, m)-convex functions

On a new class of convex functions and integral inequalities

“…Many famous inequalities can be obtained using the concept of convex functions. For details, interested readers are referred to [4][5][6][7][8][9][10][11][12][13][14]. Among these inequalities, Hermite-Hadamard's inequality, which provides us a necessary and sufficient condition for a function to be convex, is one of the most studied results.…”

Estimation-type results on the k-fractional Simpson-type integral inequalities and applications

“…Considering the Simpson type inequalities, many researches generalized and extended them. For example, Hsu et al [1], Du et al [2], Noor et al [3], İşcan et al [4] and Tunç et al [5] obtained some Simpson type inequalities for differentiable mappings which are convex, extended (s, m)-convex, geometrically relative convex, p-quasi-convex mappings and h-convex, respectively. Further results involving the Simpson type inequality in question with applications to Riemann-Liouville fractional integrals have been explored out by some scholars, including Set et al [6] and Hwang et al [7] in the study of the Simpson type inequalities using convexity, as well as İşcan [8] in the study of the Simpson type inequalities using s-convexity.…”

Generalization of Hermite-Hadamard Type Inequalities via Conformable Fractional Integrals

“…Both inequalities in (1) hold in the reverse direction if the function ℎ is concave on . In the last 60 years, many efforts have gone on generalizations, extensions, variants, and applications for the Hermite-Hadamard's inequality (see [2][3][4][5][6][7][8][9][10][11][12][13]). Anderson [14] and Sarikaya et al [15] provide the important variants for the Hermite-Hadamard's inequality.…”