Results 11 to 20 of about 8,017 (187)
Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups
Journal of Mathematical Analysis and Applications, 2003 Let \(C\) be a nonempty closed convex subset of a real Hilbert space and \(T:C\to C\) be a nonexpansive mapping. In the present paper, the authors investigate the sequence \(\{x_n\}\) generated by: \[ \begin{cases} x_0=x\in C,\\ y_n=\alpha_nx_n+ (1-\alpha_n)Tx_n,\;\alpha_n \in [0,a),\;a\in[0,1),\\ C_n=\bigl\{z\in C:\| y_n-z\|\leq\| x_n-z \| \bigr ...
Wataru Takahashi, Kazuhide Nakajo
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International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract We propose a hierarchical energy management scheme for aggregating Distributed Energy Resources (DERs) for grid flexibility services. To prevent a direct participation of numerous prosumers in the wholesale electricity market, aggregators, as self‐interest agents in our scheme, incentivize prosumers to provide flexibility. We firstly model the
Xiupeng Chen +3 more
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On Nonexpansive Mappings [PDF]
Proceedings of the American Mathematical Society, 1964 holds for all p, qEX (for all p, q with d(p, q)
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On Nonexpansive Mappings [PDF]
Proceedings of the American Mathematical Society, 1976 A generalized Hilbert space property is used to analyze nonexpansive mappings in certain settings. In particular it is shown that in l 1 {l_1} and in the important, recently defined, space J 0 {J_0} , a nonexpansive self-mapping of a bounded weak
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ORBITALLY NONEXPANSIVE MAPPINGS [PDF]
Bulletin of the Australian Mathematical Society, 2015 We define a class of nonlinear mappings which is properly larger than the class of nonexpansive mappings. We also give a fixed point theorem for this new class of mappings.
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Iterative Algorithms for Nonexpansive Mappings [PDF]
Fixed Point Theory and Applications, 2007 AbstractWe suggest and analyze two new iterative algorithms for a nonexpansive mapping T in Banach spaces. We prove that the proposed iterative algorithms converge strongly to some fixed point of T.
Yao Yonghong, Liou Yeong-Cheng
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Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems [PDF]
, 2013 We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm (AAR).
Hesse, Robert, Luke, D. Russell
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Partially nonexpansive mappings
Advances in the Theory of Nonlinear Analysis and its Application, 2022 It is defined a class of generalized nonexpansive mappings, which properly contains those defined by Suzuki in 2008, and that preserves some of its fixed point results.
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The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings [PDF]
, 2014 In this paper we provide a unified treatment of some convex minimization problems, which allows for a better understanding and, in some cases, improvement of results in this direction proved recently in spaces of curvature bounded above. For this purpose,
Ariza-Ruiz, David +2 more
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On Firmly Nonexpansive Mappings [PDF]
Proceedings of the American Mathematical Society, 1991 The author proves the following. Let X be a uniformly convex Banach space, \(C=C_ 1\cup C_ 2\cup...\cup C_ n\) a union of nonempty, bounded, closed and convex subsets of X, and T: \(C\to C\) a mapping such that \[ \| Tx-Ty\| \leq \| (1-\lambda)(x-y)+\lambda (Tx-Ty)\| \quad (x,y\in C), \] for some \(\lambda\in (0,1)\). Then T has a fixed point in C.
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