Volume 16, Issue 1
The equivalence of Ishikawa-Mann and multistep iterations in Banach space

L. Yang

Numer. Math. J. Chinese Univ. (English Ser.), 16 (2007), pp. 83-91.

Published online: 2007-02

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  • Abstract

Let $E$ be a real Banach space and

$T$ be a continuous $\Phi-$strongly accretive operator. By using a

new analytical method, it is proved that the convergence of Mann,

Ishikawa and three-step iterations are equivalent to the convergence

of multistep iteration. The results of this paper extend the results

of Rhoades and Soltuz in some aspects.


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@Article{NM-16-83, author = {L. Yang}, title = {The equivalence of Ishikawa-Mann and multistep iterations in Banach space}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2007}, volume = {16}, number = {1}, pages = {83--91}, abstract = {

Let $E$ be a real Banach space and

$T$ be a continuous $\Phi-$strongly accretive operator. By using a

new analytical method, it is proved that the convergence of Mann,

Ishikawa and three-step iterations are equivalent to the convergence

of multistep iteration. The results of this paper extend the results

of Rhoades and Soltuz in some aspects.


}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/10081.html} }
TY - JOUR T1 - The equivalence of Ishikawa-Mann and multistep iterations in Banach space AU - L. Yang JO - Numerical Mathematics, a Journal of Chinese Universities VL - 1 SP - 83 EP - 91 PY - 2007 DA - 2007/02 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nm/10081.html KW - AB -

Let $E$ be a real Banach space and

$T$ be a continuous $\Phi-$strongly accretive operator. By using a

new analytical method, it is proved that the convergence of Mann,

Ishikawa and three-step iterations are equivalent to the convergence

of multistep iteration. The results of this paper extend the results

of Rhoades and Soltuz in some aspects.


L. Yang. (1970). The equivalence of Ishikawa-Mann and multistep iterations in Banach space. Numerical Mathematics, a Journal of Chinese Universities. 16 (1). 83-91. doi:
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