Revisiting the Hermite-Hadamard fractional integral inequality via a Green function

Refinements of some fractional integral inequalities for refined $(\alpha ,h-m)$-convex function

“…The Hermite-Hadamard inequality was generalized by Riemann-Liouville fractional integrals of convex functions in [29,30]. There exist many other versions of Hermite-Hadamard inequality in literature for different kinds of fractional integrals, see [2,8,13,14,17,23,[31][32][33][34] and the references therein. In the following, we give fractional versions of Hermite-Hadamard inequalities for convex functions via Riemann-Liouville fractional integrals.…”

“…Here, motivated and inspired by the ongoing research (see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]), essentially the abovementioned works, we intend to demonstrate a few novel as well as detailed generalizations using the Riemann-Liouville operator applied over established well-known Hermite-Hadamard inequalities. More precisely, we considered the Riemann-Liouville fractional integrals with monotonically increasing function that plays a crucial role in our study.…”

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“…In this view, integral inequalities have played a significant role in narrating real-world problems. In this framework, Hermite-Hadamard inequalities are very dominant in convex theory, which has been proved by different ways and has several generalizations and extensions [9,10,11,12,13,14,15,16]. The Hermite Hadamard inequality for convex function is as follows: Let ζ : J ⊆ R → R be a convex function.…”

The Hermite–Hadamard–Jensen–Mercer Type Inequalities for Riemann–Liouville Fractional Integral

“…If ψ is concave, then (5) holds in the reversed direction. For more results associated with Hermite-Hadamard inequality, see [9][10][11][12][13][14][15][16][17][18].…”