Weak convergence of an implicit iterative process with errors for an asymptotically quasi I-nonexpansive mapping in Banach spaces [PDF]
, 2011 In this paper we prove the weak convergence of the implicit iterative process with errors to a common fixed point of an asymptotically quasi I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I in Banach ...
Mukhamedov, Farrukh +3 more
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Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces
Abstract and Applied Analysis, 2015 Let E be a smooth Banach space with a norm ·. Let V(x,y)=x2+y2-2 x,Jy for any x,y∈E, where ·,· stands for the duality pair and J is the normalized duality mapping. We define a V-strongly nonexpansive mapping by V(·,·).
Hiroko Manaka
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Strong Convergence Theorems for Nonexpansive Mapping [PDF]
Journal of Systems Science and Complexity, 2007 Let \(C\) be a closed convex subset of a uniformly smooth Banach space \(E\) and \(T\) a nonexpansive selfmap of \(C\) with \(F(T) \neq \emptyset\). Given a point \(u \in C\) and an initial guess \(x_0 \in C\), the author proves the strong convergence of the iteration scheme defined by \(z_n = \gamma_nx_n + (1 - \gamma_n)Tx_n\), \(y_n = \beta_nx_n + (1
Yongfu Su, Xiaolong Qin
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Comments on the cosmic convergence of nonexpansive maps [PDF]
Journal of Fixed Point Theory and Applications, 2021 AbstractThis note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new result for nonexpansive maps of $$\ell ^{1}$$ ℓ 1 .
Gutiérrez, Armando W., Karlsson, Anders
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A new iterative algorithm for equilibrium and fixed point problems of nonexpansive mapping [PDF]
, 2010 Nonexpansive mapping, Maximal monotone operator, Optimization problem, Equilibrium problem, Fixed point,
Yongfu Su +4 more
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Iterated nonexpansive mappings [PDF]
Journal of Fixed Point Theory and Applications, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tomás Domínguez Benavides +1 more
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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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Approximate Fixed Points for Nonexpansive and Quasi-Nonexpansive Mappings in Hyperspaces [PDF]
Fixed Point Theory and Applications, 2009 AbstractThis paper provides a few convergence results of the Ishikawa iteration sequence with errors for nonexpansive and quasi-nonexpansive mappings in hyperspaces. The results presented in this paper improve and generalize some results in the literature.
Zeqing Liu +2 more
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On the structure of the fixed-point set of a nonexpansive mapping in a Banach space [PDF]
, 1976 If C C is a closed convex subset of a reflexive, strictly convex Banach space E E , and T : C → E T:C \to E is a nonexpansive mapping which has a fixed-point in the ...
Ronald E. Bruck
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ON MULTIVALUED f-NONEXPANSIVE MAPS
Demonstratio Mathematica, 1999 The authors prove coincidence, fixed point, and convergence theorems which extend previous results by G. L. Acedo and H.-K. Xu, W. G. Dotson, G. Jungck and S. Sessa, and E. Lami Dozo.
Latif, Abdul, Tweddle, Ian
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