The Approximation of Weighted Hölder Functions by Fourier-Jacobi Polynomials to the Singular Sturm-Liouville Operator

Authors

  • Habeeb A. Aal-Rkhais Department of Mathematics, College of Computer Science and Mathematics, University of Thi-Qar, Thi-Qar, Iraq https://orcid.org/0000-0001-5692-2993
  • Ahmed H. Kamil National University of Science and Technology, Thi-Qar, Iraq https://orcid.org/0000-0002-0351-0669
  • Khalid Fanoukh Al Oweidi Department of Water Resources Management Engineering, College of Engineering, Al-Qasim Green University, Babylon, Iraq https://orcid.org/0000-0002-7592-9979

DOI:

https://doi.org/10.21123/bsj.2022.6128

Keywords:

Best approximation, Jacobi Polynomials, Moduli of smoothness, Sturm-Liouville equation, Weighted Ho ̈lder spaces

Abstract

      In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

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Published

2022-12-01

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The Approximation of Weighted Hölder Functions by Fourier-Jacobi Polynomials to the Singular Sturm-Liouville Operator. Baghdad Sci.J [Internet]. 2022 Dec. 1 [cited 2024 Mar. 29];19(6):1387. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/6128

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