id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4730	Auad, Alaa Adnan; Hilal, Mohammed A. ; Khalaf, Nihad Shareef	Best Approximation of Unbounded Functions by Modulus of Smoothness	2023	9	.pdf	application/pdf	2900	205	74	Math, 16 (2) (2023), 944-952 945 Let Lp,λ[−π, π] = {f : f is unbounded function on [−π, π], 1 ≤ p <∞}, with the norm ∥f∥Lp,λ[−π,π] = (∫ π −π |f(x)λ(x)|pdx ) 1 p <∞. Also, let N be the set of all natural numbers and for every k ∈ N ∪ {0}, we denote by Tk the set of all trigonometric polynomials of degree less than or equal to k. For a given function f ∈ Lp,λ[−π, π], we define Ek(f)Lp,λ[−π,π] = inf{∥f − g∥Lp,λ[−π,π] ; g ∈ Tk}, (1) which is called the kth degree best approximation of f with respect to Tk. Let k ∈ N and f ∈ Lp,λ[−π, π].	cache/ejpam-4730.pdf	txt/ejpam-4730.txt