Ishikawa and Mann iteration methods for nonlinear strongly accretive mappings

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

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...

On the Convergence of Mann and Ishikawa Iterative Processes for Asymptotically φ-Strongly Pseudocontractive Mappings

and Applied Analysis 3 proving: 1 a fixed point theorem for an asymptotically pseudocontractive mapping that is also uniformly L-Lipschitzian and uniformly asymptotically regular, 2 that the set of fixed points of T is closed and convex, and 3 the strong convergence of a CQ-iterative method. The literature on asymptotical-type mappings is very wide see, 7–15 . In 1967, Browder 16 and Kato 17 , ...

Stable Iteration Schemes for Local Strongly Pseudocontractions and Nonlinear Equations Involving Local Strongly Accretive Operators

Let T be a local strongly pseudocontractive and uniformly continuous operator from an arbitrary Banach space X into itself. Under certain conditions, we establish that the Noor iteration scheme with errors both converges strongly to a unique fixed point of T and is almost T -stable. The related results deal with the convergence and almost stability of the Noor iteration scheme with errors of so...