On the best convergence order of a new class of triangular summation operators

摘要

In this paper, a new class of triangular summation operators based on the equidistant nodes was constructed. It is proved that this class of operators converges uniformly to arbitrary continuous functions with the period 2π on the whole axis. Furthermore, the best approximation order and the highest convergence order are obtained. In contrast to certain operators constructed by Bernstein and Kis in the previous works, the convergence properties of the new operator constructed in this paper are superior.