Trigonometric derived rate of convergence of various smooth singular integral operators - Anastassiou, George (Modern Mathematical Methods, 2024)
In this article, we continue the study of approximation of various smooth singular integral operators. This time the foundation of our research is a trigonometric Taylor’s formula. We establish the convergence of our operators to the unit operator with rates via Jackson type inequalities engaging the first modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not positive. Our results are pointwise and uniform. The studied operators here are of the following types: Gauss-Weierstrass, Poisson-Cauchy and trigonometric.