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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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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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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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Mann iterative process for pseudocontractive mappings
Rendiconti del Circolo Matematico di Palermo, 2011The author proves that, if a strictly pseudocontractive map \(T:K\rightarrow{K}\) in the sense of \textit{F. E. Browder} and \textit{W. V. Petryshyn} [J. Math. Anal. Appl. 20, 197--228 (1967; Zbl 0153.45701)] with \(\{x\in{K}: Tx=x\}\neq{\emptyset}\) is demicompact, then the sequence \((x_{n})\) defined by \[ x_{n+1}=(1-\alpha_{n})x_{n}+\alpha_{n}Tx_{n}
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On the Mandelbrot Set of Zp+Logct via the Mann and Picard–Mann Iterations
Mathematics and Computers in Simulation, 2023Krzysztof Gdawiec +2 more
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On the Quaternion Julia Sets via Picard–Mann Iteration
Nonlinear Dynamics, 2023Krzysztof Gdawiec, Ricardo Fariello
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Multi-Step Inertial Krasnosel’skiǐ–Mann Iteration With New Inertial Parameters Arrays
Journal of Fixed Point Theory and Applications, 2021Qiao-Li Dong, Yeol Je Cho, Xiao-Huan Li
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