Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings [PDF]
Abstract and Applied Analysis, 2009 We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space.
Watcharaporn Cholamjiak, Suthep Suantai
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Abstract and Applied Analysis, 2018 We establish the existence of a strong convergent selection of a modified Mann-Reich-Sabach iteration scheme for approximating the common elements of the set of fixed points F(T) of a multivalued (or single-valued) k-strictly pseudocontractive-type ...
F. O. Isiogugu, P. Pillay, P. U. Nwokoro
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Common Fixed Points of Multistep Noor Iterations with Errors for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings [PDF]
Abstract and Applied Analysis, 2009 We introduce a general iteration scheme for a finite family of generalized asymptotically quasi-nonexpansive mappings in Banach spaces. The new iterative scheme includes the multistep Noor iterations with errors, modified Mann and Ishikawa iterations ...
S. Imnang, S. Suantai
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Strong Convergence Theorems for Strict Pseudocontractions in Uniformly Convex Banach Spaces
Fixed Point Theory and Applications, 2010 The viscosity approximation methods are employed to establish strong convergence theorems of the modified Mann iteration scheme to -strict pseudocontractions in -uniformly convex Banach spaces with a uniformly Gâteaux differentiable norm.
Lin Wei-Wei, Hu Liang-Gen, Wang Jin-Ping
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An extragradient-like approximation method for variational inequalities and fixed point problems [PDF]
Fixed Point Theory and Applications, 2011 The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem ...
Wong Ngai-Ching +3 more
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Rate of convergence of modified Mann iteration for asymptotically nonexpansive mappings [PDF]
Fixed Point Theory, 2021 The modified Mann iteration \(x_{n+1}=(1-\alpha_n) x_{n}+\alpha_n T^{n}x_{n}\) has been studied extensively for the approximation of fixed points of asymptotically nonexpansive mappings by many authors and is known to be weakly convergent in infinite-dimensional spaces.
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Approximating fixed points of a countable family of strict pseudocontractions in Banach spaces [PDF]
Opuscula Mathematica, 2014 We prove the strong convergence of the modified Mann-type iterative scheme for a countable family of strict pseudocontractions in \(q\)-uniformly smooth Banach spaces. Our results mainly improve and extend the results announced in [Y. Yao, H. Zhou, Y.-C.
Prasit Cholamjiak
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Convergence of the modified Mann's iterative method for asymptotically κ-strictly pseudocontractive mappings [PDF]
Fixed Point Theory and Applications, 2011 AbstractLet E be a real uniformly convex Banach space which has the Fréchet differentiable norm, and K a nonempty, closed, and convex subset of E. Let T : K → K be an asymptotically κ-strictly pseudocontractive mapping with a nonempty fixed point set. We prove that (I - T) is demiclosed at 0 and obtain a weak convergence theorem of the modified Mann's ...
Zhang, Ying, Xie, Zhiwei
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Strong convergence for the modified Mann’s iteration of
Applied Mathematics and Computation, 2014 In this paper, for an $λ$-strict pseudocontraction $T$, we prove strong convergence of the modified Mann's iteration defined by $$x_{n+1}=β_{n}u+γ_nx_n+(1-β_{n}-γ_n)[α_{n}Tx_n+(1-α_{n})x_n],$$ where $\{α_{n}\}$, $ \{β_{n}\}$ and $\{γ_n\}$ in $(0,1)$ satisfy: (i) $0 \leq α_{n}\leq \fracλ{K^2}$ with $\liminf\limits_{n\to\infty}α_n(λ-K^2α_n)> 0$; (ii) $
Yisheng Song 0001, Hongjun Wang
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A Modified Krasnosel’skiǐ–Mann Iterative Algorithm for Approximating Fixed Points of Enriched Nonexpansive Mappings [PDF]
Symmetry, 2022 For approximating the fixed points of enriched nonexpansive mappings in Hilbert spaces, we consider a modified Krasnosel’skiǐ–Mann algorithm for which we prove a strong convergence theorem. We also empirically compare the rate of convergence of the modified Krasnosel’skiǐ–Mann algorithm and of the simple Krasnosel’skiǐ fixed point algorithm.
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