Open AccessSome Estimates to Best Approximation of Functions by Fourier-Jacobi Differential Operators
Author(s) -
Ehsan M. Hameed,
Habeeb A. Aal-Rkhais,
Salam J. Majeed
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1095/1/012010
Subject(s) - mathematics , smoothness , moduli , jacobi polynomials , fourier transform , convergence (economics) , algebraic number , pure mathematics , differential operator , mathematical analysis , orthogonal polynomials , physics , quantum mechanics , economics , economic growth
In this paper, an extension of the idea of the best approximation in the Hölder spaces with respect to Fourier-Jacobi operators by moduli of smoothness is studied. A special form of the moduli of smoothness is considered to get a strong convergence. Further, advanced approaches of approximation and some direct and inverse results are proved. Moreover, the Jackson-type estimate of functions in Hölder spaces by Jacobi transformations to algebraic polynomials with generalized de la Vallée Poussin mean are established.