Napoles, J.Rabossi, F.2024-09-172024-09-172022-01-012306-3424https://doi.org/10.15393/j3.art.2022.11190https://hdl.handle.net/11452/44805In the present study, several new generalized integral inequalities of the Hadamard and Simpson-type are obtained. The results were obtained for functions whose first and third derivatives are either convex or satisfy the Lipschitz condition or the conditions of the Lagrange theorem. In a particular case, these results not only confirm but also improve some upper bounds, well known in the literature for the Simpson and Hermite-Hadamard-type inequali-ties.eninfo:eu-repo/semantics/openAccessHermite-hadamard typeS-convexDifferentiable mappingsSimpsons typeReal numbersDerivativesConvex functionHermite-hadamard inequalitySimp-son-type inequalityLipschitz conditionsLagrange theoremRie-mann-liouville fractional integralScience & technologyPhysical sciencesMathematicsMathematicsArticle00089056780000132311210.15393/j3.art.2022.11190