Refined inequalities of perturbed Ostrowski type for higher-order absolutely continuous functions and applications - Erden, Samet; Celik, Nuri; Khan, Muhammad Adil; Erden, Samet (Amer Inst Mathematical Sciences-Aims, 2021)
First of all, we establish an identity for higher-order differentiable functions. Then, we prove some integral inequalities for mappings that have continuous derivatives up to the order n >= 1 with n - 1 and whose n-th derivatives are the element of L-1, L-r, and L-infinity. In addition, estimates of new composite quadrature rules are examined. Finally, natural applications for exponential and logarithmic functions are given.
Keywords: Absolutely Continuous Function; Ostrowski Inequality; Perturbed Type Inequalities; Numerical Integration