منابع مشابه
Mann iteration process for monotone nonexpansive mappings
*Correspondence: [email protected] 1Department of Mathematics, Faculty of Science For Girls, King Abdulaziz University, Jeddah, 21593, Saudi Arabia Full list of author information is available at the end of the article Abstract Let (X ,‖ · ‖) be a Banach space. Let C be a nonempty, bounded, closed, and convex subset of X and T : C→ C be a monotone nonexpansive mapping. In this paper, it is ...
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This paper is a case study in proof mining applied to non-effective proofs in nonlinear functional anlysis. More specifically, we are concerned with the fixed point theory of nonexpansive selfmappings f of convex sets C in normed spaces. We study the Krasnoselski iteration as well as more general so-called Krasnoselski-Mann iterations. These iterations converge to fixed points of f only under s...
متن کاملOn the Equivalence of Mann and Ishikawa Iteration Methods
The Mann iterative scheme was invented in 1953, see [7], and was used to obtain convergence to a fixed point for many functions for which the Banach principle fails. For example, the first author in [8] showed that, for any continuous selfmap of a closed and bounded interval, the Mann iteration converges to a fixed point of the function. In 1974, Ishikawa [5] devised a new iteration scheme to e...
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The paper deals with strong convergence properties of the Mann iteration. A new class of demicontractive mappings (called α-demicontractive) is introduced for which the strong convergence of the computed sequence is assured. The paper presents also an overview of relevant contributions of the last two decades, concerning strong convergence for Mann-type iteration of demicontractive mappings.
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We show that the convergence of Mann iteration is equivalent to the convergence of Ishikawa iteration for various classes of non-Lipschitzian operators.
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ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2015
ISSN: 1023-6198,1563-5120
DOI: 10.1080/10236198.2015.1080252