We consider the convexity with respect to a pair of functions and establish a Hermite–Hadamard type inequality for Riemann–Liouville fractional integrals. Moreover, we derive some new Simpson’s and Ostrowski’s type inequalities for differentiable convex mapping with respect to a pair of functions. We also show that the newly established inequalities are the extension of some existing inequalities. Finally, we consider some mathematical examples and graphs to show the validity of the newly established inequalities.
"FRACTIONAL HERMITE–HADAMARD INEQUALITY, SIMPSON’S AND OSTROWSKI’S TYPE INEQUALITIES FOR CONVEX FUNCTIONS WITH RESPECT TO A PAIR OF FUNCTIONS." Rocky Mountain J. Math. 53 (2) 611 - 628, April 2023. https://doi.org/10.1216/rmj.2023.53.611