In this paper, we construct a new integral operator H-n,H-l(f;x) through W.
Rogosinski sum in Fourier series. The convergence order of H-n,H-l(f;x) is
the best for f(x) is an element of C-2 pi(j), 0 less than or equal to j le
ss than or equal to l, where l is arbitrary odd natural number. (C) 2001 El
sevier Science Inc. All rights reserved.