id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-1821	Al-Jubory, Abdul Khaleq O.; Salih, Shaymaa Hussain	Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation	2018	10	.pdf	application/pdf	2997	110	53	𝐼 𝑓 𝑥 𝐼 𝑘 𝑥, 𝑡 𝑢 𝑡 𝑑𝑡 ...(9) To approximate solution of eq.(1),we use the normalization polynomial basis on 𝑎, 𝑏 as: 𝑢 𝑥 ∑ 𝑎 𝑏 , 𝑥 ...(10) Where ( 𝑎 , 𝑖 0,1, … . . IHSCICONF 2017 Special Issue Ibn Al-Haitham Journal for Pure and Applied science https://doi.org/ 10.30526/2017.IHSCICONF.1821 For more information about the Conference please visit the websites: http://www.ihsciconf.org/conf/  www.ihsciconf.org   Mathematics|494    If a regular Pair 𝑋 , 𝑌 satisfies dim Xn = dim Yn and condition (H) , then the corresponding generalized projection 𝑃 satisfies: (1) for all 𝑥 ∈ 𝑋, ‖𝑃 𝑥 𝑥‖ → 0 as n→ ∞ (2) there is a constant 𝐶 0 such that, ‖𝑃 ‖ < C, n = 1,2,.. (3) for some constant 𝐶 0 independent of n, ‖𝑃 𝑥 𝑥‖ 𝐶‖𝑄 𝑥 𝑥‖ where 𝑄 𝑥 is the best approximation from X n to x. if { 𝑋 , 𝑌 } a regular pair is with a linear operator ∏ : 𝑋 ⟶ 𝑌 with ∏ 𝑋 = 𝑌 , then eq.	cache/iajs-1821.pdf	txt/iajs-1821.txt