On the Method of Successive Approximations for Nonexpansive Mappings
Simeon Reich, Itai Shafrir · 2023
Throughout this paper {x, |⋅|} denotes a (real) Banach space, x * its dual, D a closed subset of X, T: D → X a nonexpansive mapping (|Tx − Ty| ≤ |x − y| for all x and y in D), and [c n , n = 0, 1, 2, …+} a positive sequence such that 0 ∑ n = 0 ∞ c n = ∞ . https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003420040/c1be22b7-0baa-4fe4-8019-4a9594858694/content/ieq1330.tif "/> . We denote the identity operator by I, the elosure of a subset B of x by c1(B), and its distance from a point y in x by d(Y, B).