On a class of interpolation polynomials for nonlinear ordinary differential operators

This article is devoted to the construction of Lagrange interpolation formulas and formulas of Hermite type with knots of second multiplicity for ordinary differential operators of arbitrary order given in the space of continuously differentiable functions. Obtained formulas contain Stieltjes integrals and differentials Gateaux of interpolated operator. These formulas are invariant for the operator polynomials of a special class. The construction of operator interpolation formulas is based on interpolation polynomials for scalar functions.