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P A ITERATION SCHEME FOR COMMON FIXED POINTS OF TWO ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

, 2012
: In this paper, we consider a generalized iterative process and analyze a two-step iteration scheme for asymptotically nonexpansive mappings in uniformly convex Banach space.
B P Tripathi, §, M R Yadav
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Asymptotic centers and nonexpansive mappings in conjugate Banach spaces [PDF]

Pacific Journal of Mathematics, 1980
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Asymptotic behavior of iterates of nonexpansive mappings in Banach spaces, II

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1978
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Asymptotically nonexpansive mappings

Nonlinear Analysis: Theory, Methods & Applications, 1998
This is a very interesting paper. The method used suggests an entirely new approach in the study of fixed points and related properties of asymptotically nonexpansive mappings. Let \(E\) be a Banach space and \(D\subseteq E\). We recall, if there exists a sequence of reals \(\{k_i\}\) with \(k_i\downarrow 1\) such that \(\|T^ix- T^iy\|\leq k_i\|x-y\|\)
W A Kirk
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Convergence theorems for nonself asymptotically nonexpansive mappings

Computers and Mathematics With Applications, 2008
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Nawab Hussain, Safeer Hussain Khan
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On Asymptotically Nonexpansive Semigroups of Mappings

Canadian Mathematical Bulletin, 1970
A selfmapping f of a metric space (X, d) is nonexpansive (ε-nonexpansive) if d(f(x), f(y)) ≤ d(x, y) for all x, y ∊ X (respectively if d(x, y) < ε). In [1], M.
Holmes, R. D., Narayanaswami, P. P.
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Remarks on asymptotically nonexpansive mappings

Nonlinear Analysis: Theory, Methods & Applications, 2000
It is known that the uniform convexity in every direction implies the existence of fixed points for a nonexpansive mapping \(T:C\to C\) if \(C\) is assumed to be weakly compact. It is still an open problem whether this is true for asymptotically nonexpansive mappings. The purpose of the paper is to present a partial answer to this question.
Kim, Tae-Hwa, Xu, Hong-Kun
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Asymptotic Behavior of a Periodic Sequence of Nonexpansive Mappings with Applications

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2023
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Hashemi, Mehrnaz Sadat, Khatibzadeh, Hadi   +1 more
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Pythagorean Property and Asymptotic Relatively Nonexpansive Mappings

Mediterranean Journal of Mathematics, 2018
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Gabeleh, M., Markin, J.
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Asymptotic Properties of Monotonic Nonexpansive Mappings

Discrete Event Dynamic Systems, 2004
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