Approximation with an arbitrary order by modified Baskakov type operators

Given an arbitrary sequence λn > 0, n ? N , with the property that lim n ? ∞ λ n = 0 so fast as we want, in this note we consider several kinds of modified Baskakov operators in which the usual knots j n are replaced with the knots j ? λn. In this way, on each compact subinterval in 0 , + ∞ ) the order of uniform approximation becomes ω 1 ( f ; λ n ) . For example, these modified operators can uniformly approximate a Lipschitz 1 function, on each compact subinterval of 0, ∞) with the arbitrary good order of approximation λ n . Also, similar considerations are made for modified qn-Baskakov operators, with 0