On the order of the best approximation in spaces with asymmetric norm and sign-sensitive weight on classes of differentiable functions

Abstract

The class of asymmetric norms with sign-sensitive weight contains both the classical norms of the spaces and the metrics that generate one-sided approximations. For sign-sensitive weights , and an asymmetric monotone norm on the plane, we obtain an upper estimate for the number In some important cases of asymmetric norms with fixed sign-sensitive weights , we find the rate of decrease of this number as for a fixed .