Moduli of smoothness of vector valued functions of a real variable and applications

Abstract

Moduli of smoothness of Banach space valued functions of a real argument are defined and studied. The classical Whitney's theorem on the error of polynomial approximation [7] is extended to this case. Estimates for quadrature formulae and numerical treatment of abstract differential equations are presented. Applications to the numerical analysis of set-valued maps, differential inclusions and interval functions are made.