We present a new sharp Ostrowski-type inequality in the L2 norm for functions with absolutely continuous second derivative and third derivative in L2. The inequality depends on two parameters α, γ ∈ [0, 1] and generalizes the sharp inequality of Liu [1]. Special choices of parameters yield known sharp inequalities for midpoint, trapezoid, Simpson, corrected Simpson, and averaged midpoint-trapezoid rules. A complete sharpness proof is given, including explicit verification of the extremal function’s regularity. Applications to composite numerical integration are provided with explicit error bounds, and a numerical example illustrates the theoretical estimates.
