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In this chapter we continue the research on the smooth Picard singular integral operators that started in Anastassiou (Intelligent mathematics: computational analysis, 2011) see chapters 10–14. This time the foundation of our research is a parameterized 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 parameterized residual appearing term. Note that our operators are not positive. Our results are pointwise and uniform.

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Parameterized and Trigonometric Generated Quantitative Convergence of Smooth Picard Singular Integral Operators

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  • 发表日期：

    2025年

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  • George A. Anastassiou

摘要

In this chapter we continue the research on the smooth Picard singular integral operators that started in Anastassiou (Intelligent mathematics: computational analysis, 2011) see chapters 10–14. This time the foundation of our research is a parameterized 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 parameterized residual appearing term. Note that our operators are not positive. Our results are pointwise and uniform.