Approximation theory for sine series with coefficient from class supremum bounded variation sequences

The interesting problem in the Fourier series is about the monotonicity coefficients of the Fourier series, which are decreasing monotone and convergent to zero because it is one of the sufficient condition for the sine series to be uniformly convergent. A decreasing monotone of coefficient {a n } is included in the MS (Monotone Sequences) class. This class can be generalized into classes of RBVS, GMS, MBVS, SBVS by condition that the coefficients in the class provided that the sine series still uniformly convergent. In this paper we discuss approximation theory for sine series with coefficient from class supremum bounded variation sequences (SBVS).