Results 211 to 220 of about 8,281 (252)

The equivalence between Mann–Ishikawa iterations and multistep iteration

Nonlinear Analysis: Theory, Methods & Applications, 2004
In this interesting paper, the authors consider the equivalence between the one-step, two-step, three-step and multistep-iteration process for solving the nonlinear operator equations \(Tu = 0\) in a Banach space for pseudocontractive operators \(T\). It is worth mentioning that three-step iterative schemes were introduced by \textit{M. A.
Rhoades, B. E., Soltuz, Stefan M.
openaire   +2 more sources

Mann iteration with power means

Journal of Difference Equations and Applications, 2015
We analyse the recurrence xn+1=f(zn), where zn is a weighted power mean of x0,…,xn, which has been proposed to model a class of non-linear forward-looking economic models with bounded rationality. Under suitable hypotheses on weights, we prove the convergence of the sequence xn.
Bischi, G. I., Cavalli, Fausto, Naimzada, A.   +2 more
openaire   +3 more sources

New Acceleration Factors of the Krasnosel’skiĭ-Mann Iteration

Results in Mathematics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yunda Dong, Mengdi Sun
openaire   +1 more source

Fixed point approximation under Mann iteration beyond Ishikawa

Commentationes Mathematicae Universitatis Carolinae, 2020
Summary: Consider the Mann iteration \(x_{n+1}=(1-\alpha_n)x_n+\alpha_nTx_n\) for a nonexpansive mapping \(T\colon K\to K\) defined on some subset \(K\) of the normed space \(X\). We present an innovative proof of the Ishikawa almost fixed point principle for nonexpansive mapping that reveals deeper aspects of the behavior of the process.
Hester, Anthony, Morales, Claudio H.
openaire   +2 more sources

Krasnoselski-Mann Iterations in Normed Spaces

Canadian Mathematical Bulletin, 1992
AbstractWe provide general results on the behaviour of the Krasnoselski-Mann iteration process for nonexpansive mappings in a variety of normed settings.
Borwein, Jonathan, Reich, Simeon, Shafrir, Itai   +2 more
openaire   +1 more source

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
openaire   +2 more sources

Stability of Mann’s iterates under metric regularity

Applied Mathematics and Computation, 2009
This article deals with a Mann-like algorithm for solving the inclusion \[ x \in T(x)\eqno(1) \] where \(T: X \rightrightarrows X\) is a set-valued mapping defined from a Banach space \(X\) into itself. Approximate solutions to (1) are defined by \[ 0 \in \frac1{\lambda_n}(x_n - x_{n+1}) - x_n + T(x_{n+1}), \quad n = 0,1,2,\dots, \] where \(\lambda_n\)
openaire   +2 more sources

Mann Iterations with Power Means [PDF]

, 2007
In this paper we analyze a recurrence , where is a weighted power mean of ,…., . Such an iteration scheme has been proposed to model a class of non-linear forward-looking economic models ( the state today is affected by tomorrow’ s expectation ) under bounded rationality; the agents employ a recursive learning rule to update beliefs using weighted ...
Ahmad Naimzada, Gian Italo Bischi
openaire  

On Mann iteration in Hilbert spaces

Nonlinear Analysis: Theory, Methods & Applications, 2007
The author proves the strong convergence of certain Mann iterates of a hemicontractive map in a Hilbert space. Not all results, however, seem to be correct, as was pointed out by \textit{Y.\,Qing} [ibid.\ 68, No.\,2 (A), 460 (2008; Zbl 1136.47048), see the following review].
openaire   +1 more source

FIBONACCI–MANN ITERATION FOR MONOTONE ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

Bulletin of the Australian Mathematical Society, 2017
We extend the results of Schu [‘Iterative construction of fixed points of asymptotically nonexpansive mappings’, J. Math. Anal. Appl.158 (1991), 407–413] to monotone asymptotically nonexpansive mappings by means of the Fibonacci–Mann iteration process $$\begin{eqnarray}x_{n+1}=t_{n}T^{f(n)}(x_{n})+(1-t_{n})x_{n},\quad n\in \mathbb{N},\end{eqnarray ...
Alfuraidan, M. R., Khamsi, M. A.
openaire   +2 more sources