Implicit Mann fixed point iterations for pseudo-contractive mappings

摘要

Let K be a compact convex subset of a real Hilbert space H and T : K -> K a continuous hemi-contractive map. Let {a(n)}, {b(n)} and {c(n)} be real sequences in [0, 1] such that a(n) + b(n) + c(n) = 1, and {u(n)} and {v(n)} be sequences in K. In this paper we prove that, if {b(n)}, {c(n)} and {v(n)} satisfy some appropriate conditions, then for arbitrary x(0) is an element of K, the sequence {x(n)} defined iteratively by x(n) = a(n)x(n-1) + b(n)Tv(n) + C(n)u(n); n >= 1, converges strongly to a fixed point of T.