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Trigonometric generated Lp degree of approximation

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

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Annals of Communications in Mathematics 2023
, 6 (4),
Received: 09 September 2023 |
Accepted: 10 November 2023 |
Published: 31 December 2023


In this article we continue the study of smooth Picard singular integral operators that started in [3], see there chapters 10-14. This time the foundation of our research is a trigonometric Taylor’s formula. We establish the Lp convergence of our operators to the unit operator with rates via Jackson type inequalities engaging the first Lp modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not positive.


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Trigonometric generated Lp degree of approximation.

Annals of Communications in Mathematics,

6 (4):
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  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (


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