Results 171 to 180 of about 1,168,012 (202)
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On the optimal relaxation parameters of Krasnosel'ski–Mann iteration
, 2020This paper is devoted to the optimal selection of the relaxation parameter sequence for Krasnosel'ski–Mann iteration. Firstly, we establish the optimal relaxation parameter sequence of the Krasnosel'ski–Mann iteration, with which the algorithm is proved ...
Songnian He +3 more
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The equivalence between Mann–Ishikawa iterations and multistep iteration
Nonlinear Analysis: Theory, Methods & Applications, 2004In 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.
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Random Mann iteration scheme and random fixed point theorems
Applied Mathematics Letters, 2005 In this paper, some concepts such as random monotone operators, random Mann iteration and so on in a separable real Banach space are introduced. Also the existence and uniqueness theorems of random fixed points for random monotone operators satisfying ...
Li, Guozhen, Duan, Huagui
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Realization of the hybrid method for Mann iterations
Applied Mathematics and Computation, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Songnian He, Caiping Yang, Peichao Duan
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Stability of Mann’s iterates under metric regularity
Applied Mathematics and Computation, 2009This 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 \(\lambda_n\)
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On Mann iteration in Hilbert spaces
Nonlinear Analysis: Theory, Methods & Applications, 2007The 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].
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A Note on the Mann Iteration for k-Strict Pseudocontractions in Banach Spaces
, 2016We show that a variant of a previously defined function can be used to characterize 2-uniform smoothness. We then obtain greatly simplified proofs of two convergence theorems in the literature using a generalization of a lemma of and the aforementioned ...
Andrei Sipoş
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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
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A note on the convergence of Mann iteration
Creative Mathematics and Informatics, 2017The main result in this note slightly generalizes Theorem 3.4 in [S¸ t. Maruster and I. A. Rus, ˘ Kannan contractions and strongly demicontractive mappings, Creat. Math. Inform., 24 (2015), No. 3, 171–180]. We also significantly improve its proof. Both results in the paper are based on the concepts of demicontractivity and quasi-expansivity and involve
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