Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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TRIGONOMETRIC GENERATED RATE OF CONVERGENCE OF SMOOTH PICARD SINGULAR INTEGRAL OPERATORS

  • GEORGE A. ANASTASSIOU (Department of Mathematical Sciences, University of Memphis)
  • Received : 2023.09.09
  • Accepted : 2023.10.13
  • Published : 2023.11.30
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Abstract

In this article we continue the study of smooth Picard singular integral operators that started in [2], see there chapters 10-14. 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.

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References

  1. G.A. Anastassiou, Basic convergence with rates of smooth Picard singular integral operators, J. Computational Analysis and Appl. 8 (2006), 313-334.
  2. G.A. Anastassiou, Intelligent Mathematics: Computational Analysis, Springer, Heidelberg, New York, Chapter 10, 2011.
  3. G.A. Anastassiou, Opial and Ostrowski type inequalities based on trigonometric and hyperbolic type Taylor formulae, Submitted, 2023.
  4. Ali Hasan Ali, Zsolt Pales, Taylor-type expansions in terms of exponential polynomials, Mathematical Inequalities and Applications 25 (2022), 1123-1141.