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

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Habeeb A. Aal-Rkhais
Ahmed H. Kamil
Khalid F. Al Oweidi

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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Aal-Rkhais HA, Kamil AH, Al Oweidi KF. The Approximation of Weighted Ho ̈lder Functions by Fourier-Jacobi Polynomials to the Singular Sturm-Liouville Operator. Baghdad Sci.J [Internet]. [cited 2022Jun.26];:1387. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/6128
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