Trigonometric derived rate of convergence of various smooth singular integral operators

Abstract

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.

Keywords

• singular integral
• gauss-weierstrass
• poisson-cauchy and trigonometric operator
• modulus of continuity
• trigonometric taylor formula