Ishikawa and Mann Iteration Methods with Errors for Nonlinear Equations of the Accretive Type

On the equivalence of Mann and Ishikawa iteration methods with errors

We show that for several classes of mappings Mann and Ishikawa iteration procedures with errors in the sense of Xu [14] are equivalent. It is worth to mention here that, our results are the extensions or generalizations of some known recent results about equivalences.

On the Equivalence of Mann and Ishikawa Iteration Methods

The Mann iterative scheme was invented in 1953, see [7], and was used to obtain convergence to a fixed point for many functions for which the Banach principle fails. For example, the first author in [8] showed that, for any continuous selfmap of a closed and bounded interval, the Mann iteration converges to a fixed point of the function. In 1974, Ishikawa [5] devised a new iteration scheme to e...

The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces

We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of theMann iterationmethod and the Ishikawa iterationmethod for φ-pseudocontractive operators in nonempty closed convex subsets of unifor...

The equivalence of Mann iteration and Ishikawa iteration for ψ-uniformly pseudocontractive or ψ-uniformly accretive maps

Adaptive Mann iterations for nonlinear accretive and pseudocontractive operator equations

We construct adaptive Mann iterations for finding fixed points of strongly pseudocontractive mappings and solving nonlinear strongly accretive (not necessary continuous) operator equation Sx = f in p-smooth Banach spaces.