Results 131 to 140 of about 316 (157)
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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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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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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)].
Yonghong Yao, Muhammad Aslam Noor
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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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Weak and strong convergence theorems for asymptotically nonexpansive mappings
Journal of Applied Mathematics and Computing, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhao, Jing, He, Songnian
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Asymptotic Behavior of Quasi-Nonexpansive Mappings
2001Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K . We consider complete metric spaces of self-mappings of K which fix all the points of F and are quasi-nonexpansive with respect to a given convex function f on X .
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Nonexpansive Mappings, Asymptotic Regularity and Successive Approximations
Journal of the London Mathematical Society, 1978Edelstein, Michael, O'Brien, Richard C.
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