Strong Convergence of Averaged Approximants for Lipschitz Pseudocontractive Maps

On Convergence Results for Lipschitz Pseudocontractive Mappings

Strong convergence theorem for a family of Lipschitz pseudocontractive mappings in a Hilbert space

A extension of Nakajo and Takahashi’s modification of Mann’s iterative process to the Ishikawa iterative process is given. The strong convergence of a modified Ishikawa iterative scheme to a common fixed point of a finite family of Lipschitz pseudocontractive self-mappings on a closed convex subset of a Hilbert space is proved. Our theorem extends several known results. c © 2007 Elsevier Ltd. A...

Ergodic Theorem and Strong Convergence of Averaged Approximants for Non-lipschitzian Mappings in Banach Spaces

Let C be a bounded closed convex subset of a uniformly convex Banach space X and let T be an asymptotically nonexpansive in the intermediate mapping from C into itself. In this paper, we first provide a ergodic retraction theorem and a mean ergodic convergence theorem. Using this result, we show that the set F (T ) of fixed points of T is a sunny, nonexpansive retract of C if the norm of X is u...

Approximate Fixed Point Sequences and Convergence Theorems for Lipschitz Pseudocontractive Maps

Let K be a nonempty closed convex subset of a real Banach space E and T be a Lipschitz pseudocontractive self-map of K with F (T ) := {x ∈ K : Tx = x} 6= ∅. An iterative sequence {xn} is constructed for which ||xn − Txn|| → 0 as n → ∞. If, in addition, K is assumed to be bounded, this conclusion still holds without the requirement that F (T ) 6= ∅. Moreover, if, in addition, E has a uniformly G...

Convergence Theorems and Stability Results for Lipschitz Strongly Pseudocontractive Operators