Sarıkaya, Mehmet Zeki2026-07-012026-07-0120262616-4906https://doi.org/10.30538/oms2026.0302https://hdl.handle.net/20.500.12684/23078In this paper, we present new sharp forms of Iyengar-type integral inequalities for differentiable and twice-differentiable functions. Using exact integral identities and the Cauchy-Schwarz inequality, we derive optimal L2-bounds for the deviation between the midpoint value and the integral mean of a function. These results refine and extend several classical Hermite-Hadamard and Iyengar inequalities. © 2026 by the authors; licensee PSRP, Lahore, Pakistan.en10.30538/oms2026.0302info:eu-repo/semantics/openAccessConvex functionHermite-Hadamard inequalitiesIyengar inequalitymidpoint inequalitiestrapezoidArticle105185252-s2.0-105038578065N/A