The equivalence between the convergence of modified picard, modified mann, and modified ishikawa iterations

On Equivalence between Convergence of Ishikawa––mann and Noor Iterations

In this paper, we prove the equivalence of convergence between the Mann–Ishikawa– Noor and multistep iterations for Φ− strongly pseudocontractive and Φ− strongly accretive type operators in an arbitrary Banach spaces. Results proved in this paper represent an extension and refinement of the previously known results in this area. Mathematics subject classification (2010): 47H09, 47H10, 47H15.

The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range Assumption

and Applied Analysis 3 The aim of this paper is to prove the equivalence of convergent results of above Ishikawa andMann iterations with errors for generalized asymptoticallyΦ-strongly pseudocontractive mappings without bounded range assumptions in uniformly smooth real Banach spaces. For this, we need the following concepts and lemmas. Definition 1.4 see 4 . The mapping T is called generalized...

The Comparison of the Convergence Speed between Picard, Mann, Krasnoselskij and Ishikawa Iterations in Banach Spaces

Strong convergence of modified Ishikawa iterations for nonlinear mappings

In this paper, we prove a strong convergence theorem of modified Ishikawa iterations for relatively asymptotically nonexpansive mappings in Banach space. Our results extend and improve the recent results by Nakajo, Takahashi, Kim, Xu, Mat-sushita and some others.

Strong Convergence of Modified Mann Iterations for Lipschitz Pseudocontractions

In this paper, for a Lipschitz pseudocontractive mapping T, we study the strong convergence of the iterative scheme generated by ( ) (( ) ) , 1 1 1 n n n n n n n Tx u x x β + β − α + α − = + when { } { } n n α β , satisfy ( ) ; 0 lim i = α ∞ → n n ( ) ; ii 1 ∞ = α ∑ ∞ = n n ( ) . 0 lim iii = β ∞ → n n JING HAN and YISHENG SONG 148