Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps

Let K K be a nonempty closed convex subset of a real Banach space E E and T T be a Lipschitz pseudocontractive self-map of K K with F ( T ) := { x ∈ K : T x = x } ≠ ∅ F(T):=\{x∈ K:Tx=x\}≠ ∅ . An iterative sequence { x n } \{x_n\} is constructed for which | | x n − T x n | | → 0 ||x_n-Tx_n||→ 0 as n → ∞ n→ ∞ . If, in addition, K K is assumed to be bounded, this conclusion still holds without the requirement that F ( T ) ≠ ∅ . F(T)≠ ∅ . Moreover, if, in addition, E E