• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.587-603
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• 2001

The purpose of this paper is to study the nonlinear ergodic theorems and asymptotic behavior for an almost-orbit of asymptotically nonexpansive type mappings in a uniformly convex Banach space with Opial’s condition.

• East Asian mathematical journal
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• v.28 no.1
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• pp.81-92
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• 2012

The purpose of this paper is to establish strong convergence of an implicit iteration process to a common fixed point for a finite family of asymptotically quasi-nonexpansive type mappings in CAT(0) spaces. Our results improve and extend the corresponding results of Fukhar-ud-din et al. [15] and some others from the current literature.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.525-536
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• 2007

In this paper, we prove the weak and strong convergence of the Noor iterative scheme to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• East Asian mathematical journal
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• v.29 no.1
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• pp.23-37
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• 2013

The purpose of this paper is to study an implicit iteration process with errors and establish weak and strong convergence theorems to converge to common fixed points for a finite family of generalized asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve and generalize some known results from the existing literature.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.131-137
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• 1996

In this paper, we give a necessary and sufficient condition for the weak convergence of trajectories of non-lipschitzian asymptotically nonexpansive mappings.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.667-674
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• 2009

In this paper, a new one-step iterative scheme with error for approximating common fixed points of asymptotically quasi-nonexpansive type nonself-mappings in Banach space is defined. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al.,(2007), namely, A new iterative algorithm for approximating common fixed points for asymptotically non-expansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others.

• East Asian mathematical journal
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• v.26 no.3
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• pp.337-350
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• 2010

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.473-482
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• 2011

In this paper, mappings which are asymptotically pseudo-contractive in the intermediate sense are considered based on a hybrid projection method. Strong convergence theorems of fixed points are established in the framework of Hilbert spaces.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.847-860
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• 2006

In this paper, some new convergence theorems of the modified Ishikawa and Mann iterative sequences with errors for asymptotically set-valued pseudocontractive mappings in uniformly smooth Banach spaces are given.

• East Asian mathematical journal
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• v.25 no.4
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• pp.415-423
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• 2009

In this paper, we consider the hybrid monotone projection algorithm for asymptotically quasi-pseudocontractive mappings. A strong convergence theorem is established in the framework of Hilbert spaces. Our results mainly improve the corresponding results announced by [H. Zhou, Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces, Nonlinear Anal. 70 (2009) 3140-3145] and also include Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152; Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal. 68 (2008) 2828-2836] as special cases.