An Iterative Scheme for the Approximations of Fixed Points of Asymptotically Pseudocontractive Mappings
Arif Rafiq · Numerical Functional Analysis and Optimization · 2011
Let K be a nonempty closed convex subset of a real Banach space E, T: K → K a uniformly continuous asymptotically pseudocontractive mapping having T(K) bounded with sequence {k n } n ≥ 0 ⊂ [1, ∞), lim n→∞ k n = 1 such that p ∈ F(T) = {x ∈ K: Tx = x}. Let {α n } n ≥ 0 ∈ [0, 1] be such that and lim n→∞α n = 0. For arbitrary x 0 ∈ K and {v n } n ≥ 0 in K, define the sequence {x n } n ≥ 0 by satisfying lim n→∞‖v n − x n ‖ = 0. Then {x n } n ≥ 0 converges strongly to p ∈ F(T).