id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6311	Panma, Sayan; Suparatulatorn, Raweerote; Chaobankoh, Tanadon	Fixed Point Techniques for Graph-Based Mappings with Image Recovery Approach	2025	20	.pdf	application/pdf	6407	390	72	∥xn − x∗∥2 + 2|βn|∥xn − xn−1∥∥dn − x∗∥ − (1− σi n)η i n(1− µi n)µ i n∥dn − Jidn∥2. Now, for any i = 1, 2, . . . , N, from Proposition 1, we have the inequalities: ∥Jicin − x∗∥2 ≤ ∥cin − x∗∥2 = ∥(1− µi n)dn + µi nJidn − x∗∥2 = ∥(1− µi n)(dn − x∗) + µi n(Jidn − x∗)∥2 = (1− µi n)∥dn − x∗∥2 + µi n∥Jidn − x∗∥2 − (1− µi n)µ i n∥dn − Jidn∥2 ≤ (1− µi n)∥dn − x∗∥2 + µi n∥dn − x∗∥2 − (1− µi n)µ i n∥dn − Jidn∥2 = ∥dn − x∗∥2 − (1− µi n)µ i n∥dn − Jidn∥2, and ∥Jibin − x∗∥2 ≤	cache/ejpam-6311.pdf	txt/ejpam-6311.txt