id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5744	Mohammad Akram	A Four-Step Semi-Implicit Midpoint Approximation Scheme for Fixed Point with Applications	2025	19	.pdf	application/pdf	7371	585	80	− ϱ ∥∥∥] ≤ εk 2 (∥ϱk − ϱ∥+ ∥θk − ϱ∥), where εk = (1− γk + τγk), which turns after simplification into ∥θk − ϱ∥ ≤ εk (2− εk) ∥ϱk − ϱ∥. (15) − ϱ ∥∥∥+ βkτ ∥∥∥(ϑk + θk 2 ) − ϱ ∥∥∥ ≤ τ 2 ∥ϑk − ϱ∥+ τ 2 [(1− βk)∥ϱk − ϱ∥+ βk∥θk − ϱ∥], which yields into ∥ϑk − ϱ∥ ≤ τ (2− τ)	cache/ejpam-5744.pdf	txt/ejpam-5744.txt