In this paper we prove two theorems on the degree of approximation of continuous functions by matrix means related to partial sums of a Fourier series in the Holder metric.These theorems can be taken as counterparts o...In this paper we prove two theorems on the degree of approximation of continuous functions by matrix means related to partial sums of a Fourier series in the Holder metric.These theorems can be taken as counterparts of those previously obtained by T.Singh[3].展开更多
The pointwise estimates of the deviation Tn,A,Bf（·） -- f（·） in terms of moduli of continuity w. f and w. f there are proved. Analogical results on norm approximation with remarks and corollaries are also...The pointwise estimates of the deviation Tn,A,Bf（·） -- f（·） in terms of moduli of continuity w. f and w. f there are proved. Analogical results on norm approximation with remarks and corollaries are also given. In the results there are used the essentially weaker conditions than these in [Mittal, M. L.： J. Math. Anal. Appl., 220, 434-450） （1998） Theorem 1, p. 4377.展开更多
文摘In this paper we prove two theorems on the degree of approximation of continuous functions by matrix means related to partial sums of a Fourier series in the Holder metric.These theorems can be taken as counterparts of those previously obtained by T.Singh[3].
文摘The pointwise estimates of the deviation Tn,A,Bf（·） -- f（·） in terms of moduli of continuity w. f and w. f there are proved. Analogical results on norm approximation with remarks and corollaries are also given. In the results there are used the essentially weaker conditions than these in [Mittal, M. L.： J. Math. Anal. Appl., 220, 434-450） （1998） Theorem 1, p. 4377.
