Jianqiang XieMuhammad Aamir AliHŸseyin BudakMichal Fe_kanThanin Sitthiwirattham2025-03-102025-03-102023Rocky Mountain Journal of Mathematics35759610.1216/rmj.2023.53.6112-s2.0-85166416902https://repository.dusit.ac.th//handle/123456789/4550We consider the convexity with respect to a pair of functions and establish a HermiteÐHadamard type inequality for RiemannÐLiouville fractional integrals. Moreover, we derive some new SimpsonÕs and OstrowskiÕs 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. © Rocky Mountain Mathematics Consortium.(g,h)-convex functionsfractional calculusHermiteÐHadamard inequalityOstrowskiÕs inequalitySimpsonÕs inequalityArticleScopus