The Asymptotic Behavior of Firmly Nonexpansive Mappings
نویسندگان
چکیده
منابع مشابه
The Asymptotic Behavior of Firmly Nonexpansive Mappings
We present several new results on the asymptotic behavior of firmly nonexpansive mappings in Banach spaces and in the Hubert ball. Let D be a subset of a (real) Banach space X. Recall that a mapping T: D -» X is said to be firmly nonexpansive [2, 4] if for each x and y in D, the convex function /: [0,1] -> [0, oo) defined by f{s) = \(\-s)x + sTx-((l-s)y + sTy) \ is nonincreasing. Note that T is...
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*Correspondence: [email protected] 1Department of Economics, Chiba University, Yayoi-cho, Inage-ku, Chiba-shi, Chiba, 263-8522, Japan Full list of author information is available at the end of the article Abstract We show that a strongly relatively nonexpansive sequence of mappings can be constructed from a given sequence of firmly nonexpansive-like mappings in a Banach space. Using this ...
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In this paper, two examples of quasi-firmly type nonexpansive mappings are given to prove that the concept is different from nonexpansive mapping. Furthermore, it is studied to the convergence of the sequence of successive approximations for this class of mappings only when the super limit of iteration coefficients is less than 1. In particular, the Picard iteration {T x0} of such a mapping con...
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Recently, S. Reich and S. Simons provided a novel proof of the Kirszbraun-Valentine extension theorem using Fenchel duality and Fitzpatrick functions. In the same spirit, we provide a new proof of an extension result for firmly nonexpansive mappings with an optimally localized range. Throughout this paper, we assume that X is a real Hilbert space, with inner product p = 〈· | ·〉 and induced norm...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1987
ISSN: 0002-9939
DOI: 10.2307/2045990