The equivalence of Mann iteration and Ishikawa iteration forψ-uniformly pseudocontractive orψ-uniformly accretive maps

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

The Equivalence of Mann and Ishikawa Iterations Dealing with Ψ−uniformly Pseudocontractive Maps without Bounded Range

We prove that Mann and Ishikawa iterations are equivalent models dealing with ψ-uniformly pseudocontractive or d-weakly contractive maps without bounded range.

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 Non-lipschitzian Operators

We show that the convergence of Mann iteration is equivalent to the convergence of Ishikawa iteration for various classes of non-Lipschitzian operators.