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, IraqFollow
Ahmed H. Kamil, National University of Science and Technology, Thi-Qar, IraqFollow
Khalid Fanoukh Al Oweidi, Department of Water Resources Management Engineering, College of Engineering, Al-Qasim Green University, Babylon, IraqFollow

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.

Keywords

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

Article Type

Article

How to Cite this Article

Aal-Rkhais, Habeeb A.; Kamil, Ahmed H.; and Al Oweidi, Khalid Fanoukh (2022) "The Approximation of Weighted Hölder Functions by Fourier-Jacobi Polynomials to the Singular Sturm-Liouville Operator," Baghdad Science Journal: Vol. 19: Iss. 6, Article 6.
DOI: https://doi.org/10.21123/bsj.2022.6128