Riemann-Liouville fractional Hermite-Hadamard inequalities. Part II: for twice differentiable geometric-arithmetically s-convex functions

Abstract

Motivated by the definition of geometric-arithmetically s-convex functions in (Shuang et al. in Analysis 33:197-208, 2013) and second-order fractional integral identities in (Zhang and Wang in

Riemann-Liouville fractional trapezium-like inequalities via generalized (m, h 1 , h 2 )-preinvexity

“…For example, refer to [4,6,11,10,12,27,32] for convex functions, to [34,40] for m-convex functions, to [1] for (s, m)-convex functions, to [35] for r-convex functions, to [5,14] for harmonically convex functions, to [13] for quasi-geometrically convex functions, to [20] for GA-s-convex functions, to [25,30] for preinvex functions, to [8] for generalized (α, m)-preinvex functions, to [15] for MT m -preinvex functions, to [3] for s-Godunova-Levin functions, to [22] for h-convex functions and see the references cited therein.…”

Fractional Hermite-Hadamard-like type inequalities for convex functions

“…In the caes of α = 1, the fractional integrals reduces to the classical integral. Recently, many authors have studied a number of inequalities by used the Riemann-Liouville fractional integrals, you may see [1][2][3][4][5][6][7][8][9][10][13][14][15][16][17][18][19][20] and the references cited therein.…”

Generalized Simpson-like type integral inequalities for differentiable convex functions via Riemann-Liouville integrals

“…In the caes of α = 1, the fractional integrals reduces to the classical integral. Recently, many authors have studied a number of inequalities by used the Riemann-Liouville fractional integrals, see [1][2][3][4][5][6][7][8][9][10]13,[15][16][17][18] and the references cited therein.…”