Home 9 Volume 9 Trigonometric generated Lp degree of approximation
Open AccessArticle
Trigonometric generated Lp degree of approximation

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

* Corresponding Author
Annals of Communications in Mathematics 2023
, 6 (4),
209-219.
https://doi.org/10.62072/acm2023060401
Received: 09 September 2023 |
Accepted: 10 November 2023 |
Published: 31 December 2023

Abstract

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.

Keywords

Cite This Article

George A. Anastassiou.
Trigonometric generated Lp degree of approximation.

Annals of Communications in Mathematics,

2023,
6 (4):
209-219.
https://doi.org/10.62072/acm2023060401
References

[1] Ali Hasan Ali and Zsolt Pales. Taylor-type expansions in terms of exponential polynomials, Mathematical ´ Inequalities & Applications, 25(4) (2022), 1123-1141.
[2] George A. Anastassiou. Basic convergence with rates of smooth Picard singular integral operators, J. Computational Analysis and Appl., 8(4) (2006), 313-334.
[3] George A. Anastassiou. Intelligent Mathematics: Computational Analysis, Springer, Heidelberg, New York, Chapter 12, 2011.
[4] George A. Anastassiou. Opial and Ostrowski type inequalities based on trigonometric and hyperbolic type Taylor formulae, submitted, 2023.
[5] Ali Hasan Ali and Zsolt Pales. Taylor-type expansions in terms of exponential polynomials, Mathematical ´ Inequalities & Applications, 25(4) (2022), 1123-1141.
[6] Carlo Bardaro, Ilaria Mantellini, Gumrah Uysal, Basar Yilmaz. A class of integral operators that fix exponential functions, Mediterr. J. Math. 18 (2021), no. 5, Paper No. 179, 21 pp.
[7] Ozge Ozalp Guller, G ¨ umrah Uysal. On certain multidimensional nonlinearintegrals, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 69 (2020), no. 2, 1356-1367.
[8] Gumrah Uysal, Hemen Dutta. On weighted convergence of double singular integral operators involving summation, Applied mathematical analysis: theory, methods, and applications, 579-603, Stud. Syst. Decis. Control 177, Springer, Cham, 2020.
[9] Gumrah Uysal. On nonlinear bivariate [m1,m2]-singular integral operators, Math. Methods Appl. Sci. 42 (2019), no. 16, 5455-5467.

  • Creative Commons License
  • 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 (https://creativecommons.org/licenses/by/4.0/).

    0 Comments

    Submit a Comment

    Your email address will not be published. Required fields are marked *

    Preview PDF

    XML File

    Loading

    Share