Results 141 to 150 of about 1,226,787 (172)
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Asymptotic behavior for asymptotically nonexpansive mappings
Nonlinear Analysis: Theory, Methods & Applications, 1996Let \(X\) be a Banach space. Suppose that \(X\) has the Opial (or locally uniform Opial) property and the norm of \(X\) is UKK (uniform Kadec-Klee). Let \(C\) be a weakly compact convex subset of \(X\), and let \(T\) be an asymptotically nonexpansive self-mapping of \(C\) in the weak sense.
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Viscosity approximation methods for asymptotically nonexpansive mappings
Applied Mathematics and Computation, 2008The iteration method \(x_{n+1}=\alpha_n f(x_n) + \beta_n x_n + \gamma_n T^nx_n\) is discussed for approximating a special fixed point of an asymptotically nonexpansive mapping \(T\) defined on a uniformly convex Banach space with uniformly Gâteaux differentiable norm.
Jian Lou, Li-juan Zhang, Zhen He
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On the asymptotic regularity of nonexpansive mappings
Acta Mathematica Hungarica, 1986Given a normed vector space X, a self-mapping P of X is said to be asymptotically regular if for every point x of X we have \(\| P^{n+1}x-P^ nx\| \to 0\) as \(n\to \infty\). First, a new and simple proof is given to the theorem of S. Ishikawa, namely: Theorem B: Let D be a subset of a normed space X and \(T: X\to X\) be a nonexpansive mapping.
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On hybrid projection methods for asymptotically quasi--nonexpansive mappings
Applied Mathematics and Computation, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaolong Qin +2 more
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Nonexpansive mappings and asymptotic regularity
Nonlinear Analysis: Theory, Methods & Applications, 2000The present paper is devoted to a new approach to asymptotic regularity of nonexpansive mappings in Banach spaces. The results are established for the larger class of directionally nonexpansive mappings and extend or complement those of \textit{M. Edelstein} [Am. Math. Mon. 73, 509-510 (1966; Zbl 0138.39901)], \textit{M. Edelstein} and \textit{R. C.
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On Asymptotic Centers and Fixed Points of Nonexpansive Mappings
Canadian Journal of Mathematics, 1980Let X be a Banach space and B a bounded subset of X. For each x ∈ X, define R(x) = sup{‖x – y‖ : y ∈ B}. If C is a nonempty subset of X, we call the number R = inƒ{R(x) : x ∈ C} the Chebyshev radius of B in C and the set the Chebyshev center of B in C.
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Convergence of three-step iterations for asymptotically nonexpansive mappings
Applied Mathematics and Computation, 2007A general three-step fixed-point iteration for asymptotically nonexpansive mappings in a Banach space is studied. The method includes the (modified) Noor and Ishikawa iteration schemes [cf. \textit{B. Xu} and \textit{M. Aslam Noor}, J. Math. Anal. Appl. 267, No.~2, 444--453 (2002; Zbl 1011.47039)].
Muhammed Aslam Noor, Yonghong Yao
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Demiclosedness principle and asymptotic behavior for asymptotically nonexpansive mappings
Nonlinear Analysis: Theory, Methods & Applications, 1995The demiclosedness principle of \textit{F. E. Browder} [Bull. Am. Math. Soc. 74, 660-665 (1968; Zbl 0164.44801)] states that if \(X\) is a uniformly convex Banach space, if \(C\) is a nonempty closed convex subset of \(X\), and if \(T:C\to X\) is a nonexpansive map, then \(I-T\) is demiclosed at each \(y\) in \(X\).
Lin, Pei-Kee +2 more
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FIBONACCI–MANN ITERATION FOR MONOTONE ASYMPTOTICALLY NONEXPANSIVE MAPPINGS
Bulletin of the Australian Mathematical Society, 2017We extend the results of Schu [‘Iterative construction of fixed points of asymptotically nonexpansive mappings’, J. Math. Anal. Appl.158 (1991), 407–413] to monotone asymptotically nonexpansive mappings by means of the Fibonacci–Mann iteration process $$\begin{eqnarray}x_{n+1}=t_{n}T^{f(n)}(x_{n})+(1-t_{n})x_{n},\quad n\in \mathbb{N},\end{eqnarray ...
Alfuraidan, M. R., Khamsi, M. A.
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Approximating solutions of variational inequalities for asymptotically nonexpansive mappings
Applied Mathematics and Computation, 2009Let \(E\) be a real Banach space with a uniformly Gâteaux differentiable norm and possessing a uniform normal structure. Iterative sequences are constructed which involve a contractive and an asymptotically nonexpanding mappings \(K\to K\), where \(K\) is a bounded closed convex subset of \(E\).
Shih-Sen Chang +3 more
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