id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ma-27	Ofem, Austine Efut; Udofia, Unwana Effiong; Igbokwe, Donatus Ikechi	New Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem	2021	27	.pdf	application/pdf	8870	539	76	− z‖ = x. (4.7) Again, using (1.7), we get ‖`s+1 − z‖ = ‖Tζs − z‖ ≤ ‖ζs − z‖ = ‖Tws − z‖ ≤ ‖ws − z‖ = ‖(1− δs)T`s + δsTgs − z‖ ≤ (1− δs)‖T`s − z‖+ δs‖Tgs − z‖ ≤ (1− δs)‖`s − z‖+ δs‖gs − z‖ = ‖`s − z‖ − δs‖`s − z‖+ δs‖gs − z‖. (4.8) From (4.8), we have ‖`s+1 − z‖ − ‖`s − z‖ δs ≤ ‖gs − z‖ − ‖`s − z‖. (4.9) − z‖ ≤ γ(1− δs)‖`s − z‖+ γδs(1− (1− γ)βs)‖`s − z‖ = γ(1− (1− γ)δsβs)‖`s − z‖. (3.2) From (1.7) and (3.2), we obtain ‖ζs − z‖ = ‖Tws − z‖ ≤ γ‖ws − z‖ ≤ γ2(1− (1− γ)δsβs)‖`s − z‖. (3.3) Using (1.7) and (3.3), we have ‖`s+1 − z‖ = ‖Tζs − z‖ ≤ γ‖ζs − z‖ ≤ γ3(1− (1− γ)δsβs)‖`s − z‖. (3.4) From (3.4), we have the following inequalities: ‖`s+1 − z‖ ≤ γ3(1− (1− γ)δsβs)‖`s − z‖ ≤ γ3(1− (1− γ)δs−1βs−1)‖`s−1 − z‖... ‖`1	cache/ma-27.pdf	txt/ma-27.txt