id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ijassa-306	Suantai, Suthep; Cholamjiak, Watcharaporn	Monotone Hybrid Methods for a Finite Family of Nonexpasive Multi-valued Maps and Equilibrium Problems	2011	14	.pdf	application/pdf	5782	346	84	− un‖ → 0 as n→∞, ∀i = 1, 2, ...,m. (8) From Lemma 2.7, we obtain ‖un − v‖2 = ‖Trnxn − Trnv‖2 ≤ 〈Trnxn − Trnv, xn − v〉 = 〈un − v, xn − v〉 = 1 2 { ‖un − v‖2 + ‖xn − v‖2 − ‖xn − un‖2 } , hence ‖un − v‖2 ≤ ‖xn − v‖2 − ‖xn − un‖2. − αjα1g(‖xj − x1‖) ‖α1x1 + α3x3 + α4x4 + ...+ α2x2‖2 ≤ m∑ i=1 αi‖xi‖2 − αjα2g(‖xj − x2‖) ... ‖α1x1 + α4x4 + α5x5 + ...+ α3x3‖2 ≤ m∑ i=1 αi‖xi‖2 − αjαj−1g(‖xj − xj−1‖) ‖α1x1 + α4x4 + α5x5 + ...+ α3x3‖2 ≤ m∑ i=1 αi‖xi‖2 − αjαj+1g(‖xj − xj+1‖) ... ‖α1x1 + αmxm + α2x2 + ...+ αm−1xm−1‖2 ≤ m∑ i=1 αi‖xi‖2 − αjαmg(‖xj − xm‖).	cache/ijassa-306.pdf	txt/ijassa-306.txt