Simple projection algorithm for a countable family of weak relatively nonexpansive mappings and applications
Jingling Zhang, Yongfu Su, Qingqing Cheng · Fixed Point Theory and Applications · 2012
Abstract Let E be a uniformly convex and uniformly smooth Banach space, let C be a nonempty closed convex subset of E, let { T n } : C → C be a countable family of weak relatively nonexpansive mappings such that F = ⋂ n = 1 ∞ F ( T n ) ≠ ∅ . For any given gauss x 0 ∈ C , define a sequence { x n } in C by the following algorithm: { C 0 = C , C n + 1 = { z ∈ C n : ϕ ( z , T n x n ) = ϕ ( z , x n ) } , n = 0 , 1 , 2 , 3 , … , x n + 1 = Π C n + 1 x 0 . Then { x n } converges strongly to q = Π F x 0 . MSC:47H05, 47H09, 47H10.