A new iteration process for generalized Lipschitz pseudo-contractive and generalized Lipschitz accretive mappings

✍ Scribed by C.E. Chidume; E.U. Ofoedu

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 175 KB
• Volume: 67
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.05.012

✦ Synopsis

Let K be a nonempty closed convex subset of a real Banach space E. Let T : K → K be a generalized Lipschitz pseudo-contractive mapping such that F(T ) := {x ∈ K : T x = x} = ∅. Let {α n } n≥1 , {λ n } n≥1 and {θ n } n≥1 be real sequences in (0, 1) such that α n = o(θ n ), lim n→∞ λ n = 0 and λ n (α n + θ n ) < 1. From arbitrary x 1 ∈ K , let the sequence {x n } n≥1 be iteratively generated by

Then, {x n } n≥1 is bounded. Moreover, if E is a reflexive Banach space with uniformly Gâteaux differentiable norm and if ∞ n=1 λ n θ n = ∞ is additionally assumed, then, under mild conditions, {x n } n≥1 converges strongly to some x * ∈ F(T ).