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Equivalence of Modified Mann and Multi-step Noor Iteration Methods with Errors

2009 International Conference on Computational Intelligence and Natural Computing, 2009
The equivalence of the strong convergence between the modified Mann and multi-step Noor iterations with errors is proved for uniformly Lipchitzian generalized strongly successively asymptotically Q-pseudocontractive operators in arbitrary real Banach space.
Ren-Xing Ni
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Δ-Convergence of the Modified Mann Iteration in Complete CAT(0) Spaces

Vietnam Journal of Mathematics, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hadi Khatibzadeh, Sajad Ranjbar, Khatibzadeh Hadi   +2 more
exaly   +3 more sources

Strong convergence and certain control conditions for modified Mann iteration

Nonlinear Analysis: Theory, Methods & Applications, 2008
In this paper, the authors propose a new modified Mann iteration for computing fixed points of nonexpansive mappings in a Banach space setting. This new iterative scheme combines the modified Mann iteration introduced by \textit{T.\,H.\thinspace Kim} and \textit{H.\,K.\thinspace Xu} [``Strong convergence of modified Mann iterations'', Nonlinear Anal ...
Yonghong Yao, Rudong Chen
exaly   +2 more sources

Convergence of the modified Mann’s iteration method for asymptotically strict pseudo-contractions

Nonlinear Analysis: Theory, Methods & Applications, 2008
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Hong-Kun Xu
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Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces

Journal of Mathematical Analysis and Applications, 2013
Let (M,d) be a complete 2-uniformly convex metric space. Let C be a nonempty, bounded, closed, and convex subset of M, and let T:C→C be an asymptotic pointwise nonexpansive mapping. In this paper, we prove that the modified Mann iteration process defined
Mohamed A Khamsi
exaly   +2 more sources

The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps

Journal of Mathematical Analysis and Applications, 2004
The convergence of modified Mann iteration is equivalent to the convergence of modified Ishikawa iterations, when T is an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive ...
B E Rhoades, Stefan M Soltuz
exaly   +2 more sources

Strong convergence of modified Mann iterations

Nonlinear Analysis: Theory, Methods & Applications, 2005
Let \(X\) be a real Banach space with a norm \(\|\cdot\|\) and let \(C\) be a nonempty, closed and convex subset of \(X\). A mapping \(T:C\to C\) is nonexpansive provided that \(\| Tx- Ty\|\leq\| x-y\|\) for all \(x,y\in C\). Assume that \(T\) has at least one fixed point in \(C\). The authors consider the following iteration sequence \(\{x_n\}\) for \(
Kim, Tae-Hwa, Xu, Hong-Kun
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A modified successive projection method for Mann’s iteration process

Journal of Fixed Point Theory and Applications, 2018
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He, Songnian, Yang, Zhuo
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Modified mann iterations for nonexpansive semigroups in Banach space

Acta Mathematica Sinica, English Series, 2010
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Chen, Ru Dong, He, Hui Min, Noor, Muhammad Aslam   +2 more
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Fixed point theorems of modified Mann and Ishikawa iterations

Journal of Interdisciplinary Mathematics, 2020
In this paper, we prove fixed point results of asymptotically nonexpansive mappings in uniformly convex Banach spaces under Fibonacci-Mann and Ishikawa iterations also prove some results weak conve...
openaire   +1 more source