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.
This article introduces and analyzes a new class of integral inequalities relating the integrals of two functions over different intervals. Using classical tools such as the Hermite-Hadamard, Steffensen and Young integral inequalities, we derive several refined bounds under monotonicity and convexity assumptions.
This article makes a contribution to the ongoing development of the Steffensen integral inequality by presenting two new results. The first result generalizes the classical Steffensen integral inequality by introducing an additional function that combines key aspects of the Steffensen and Chebyshev integral inequalities. The second result presents a concave integral inequality derived using integration techniques. Numerical examples are provided to demonstrate the validity and application of the results.
