A note on the best approximation of sine and cosine series

摘要

Recently we extended some interesting theorems of Konyushkov giving estimations for the best approximation by the coefficients of the Fourier series of the function in question. We replaced the monotone or quasi-monotone coefficient sequences by coefficient sequences of rest bounded variation. In this note both notions are generalized for such coefficient sequences where certain restriction is given only in terms of the "rest variation" of the sequence.