id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6583	Albeladi, Ghadah; Omran, Saleh 	A Natural Extension of the Banach Fixed Point Theorem in a b-Metric Space with an Orthogonal Direct Sum Structure	2025	27	.pdf	application/pdf	9335	506	84	Let Rd denotes the orthogonal direct sum R ⊕ R ⊕ · · · ⊕ R of d-copies of R. Let R⊕d be the direct sum set, and x, y ∈ R⊕d , x = (x1, x2, · · · , xd), y = (y1, y2, · · · , yd) by x ≾ y (respectively, xi < yi) for all i = 1, 2, · · · d. In addition, R⊕d + = {x ∈ R⊕d : xi ≥ 0, ∀i = 1, 2, · · · , d} is the set of positive elements in R⊕d , and we denote x ≿ 0̃ if xi ≥ 0 for all i = 1, 2, · · · , d, where 0̃ is the d× d zero matrix in R⊕d .	cache/ejpam-6583.pdf	txt/ejpam-6583.txt