The Convergence of Some Positive Linear Operators on the Space of Multivariate Continuous Periodic Functions

As a consequence of a general result, we prove that in the case of singular integrals the set of convergence consists only of the two functions \(\textbf{1}\) $\mathbf{1}$ and \(\cos \) $cos$ . We prove also a multivariate version of this result and apply it to find the necessary and sufficient conditions for the convergence of the sequences of positive linear operators associated to the rectangular and triangular summation.