On a linear combination of S.N. Bernstein trigonometric interpolation polynomial

摘要

In this paper a new trigonometric polynomial operator through S.N. Bernstein trigonometric interpolation polynomial is constructed. It converges for each f(x)∈C2π uniformly on (−∞,+∞), and has the best approximation order, and its saturation order is 1/nr+1 (where r is an odd natural number).