New error inequalities for the Lagrange interpolating polynomial

Many error inequalities in polynomial interpolation can be found in [1, 7]. These error bounds for interpolating polynomials are usually expressed by means of the norms ‖ · ‖p, 1≤ p ≤∞. Some new error inequalities (for corrected interpolating polynomials) are given in [10, 11]. The last mentioned inequalities are similar to error inequalities obtained in recent years in numerical integration and they are known in the literature as inequalities of Ostrowski (or Ostrowski-like, Ostrowski-Grüss) type. For example, in [9] we can find inequalities of Ostrowski-Grüss type for the well-known Simpson’s quadrature rule, ∣∣∣ ∫ x2 x0 f (t)dt− h 3 [ f ( x0 ) +4 f ( x1 ) + f ( x2 )]∣∣∣≤ Cn(Γn− γn)hn+1, (1.1)