ON UNIFORM APPROXIMATION OF ABSTRACT FUNCTIONS ON CONVEX POLYGONS

摘要

Approximation aggregates of summatory type are constructed for functions f : Q → X, where Q is a convex polygon in R~2 and X is a real Banach space. An assertion providing an accuracy estimate for an uniform approximation in terms of the modulus of continuity of the second order for f is proved. Differential properties of such aggregates are studied. Bibliography. 7 titles.