WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
One – Sided Approximation in $$L_p$$ (X)
Author:
Abstract: The aim of this research to study the approximation of functions in the space- $$L_{p}$$ by the “algebraic polynomial” in terms of the” average modulus” of the k-order also, we will estimate the degree of the (O-S- A), (means one – sided approximation) in term of averaged modulus where all the results which number is eleven we need to prove the main theorem that (the degree of best (O-S- A) of $$f$$ by trigonometric polynomials of order n in $$L_p (X),( \widetilde{E}_{n}(f)_p)$$ is less than or equal to (Averaged modulus of smoothness of $$f$$ of order- $$k,(τ_{k}(f, \frac{1}{n})_{p})$$) have been proven, It has also been proven the converse theorem for the main theorem in this research.
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Keywords: Modulus of continuity, local of smoothness, trigonometric polynomials, average modulus, degree of best approximation, periodic functions
Pages: 940-947
DOI: 10.37394/23206.2024.23.97