• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.133-142
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• 2008

In this paper, we prove two strong convergence theorems for asymptotically nonexpansive mappings in Hibert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo, Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], Kim, 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], Martinez-Yanes, Xu [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and some others.

• 대한수학회논문집
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• 제31권3호
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• pp.483-493
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• 2016

In this paper, we study and prove common fixed point theorems for N generalized I-asymptotically nonexpansive mappings in a Hadamard space.

• East Asian mathematical journal
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• 제19권1호
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• pp.103-111
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• 2003

In this paper, we will discuss some sufficient and necessary conditions for modified Ishikawa iterative sequence with mixed errors to converge to fixed points for asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend, generalize and improve the corresponding results in Liu [4,5] and Ghosh-Debnath [2].

• 충청수학회지
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• 제21권3호
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• pp.327-337
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• 2008

In this paper, we prove strong convergence theorems of Halpern iteration for relatively asymptotically nonexpansive mappings in the framework of Banach spaces. Our results extend and improve the recent ones announced by [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006), 2400-2411], [X. Qin, Y. Su, Strong convergence theorem for relatively nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007), 1958-1965] and many others.

• 대한수학회논문집
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• 제29권1호
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• pp.83-95
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• 2014

In a uniformly convex Banach space, we introduce a iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings and utilize a new inequality to prove several convergence results for the iterative sequence. The results generalize and unify many important known results of relevant scholars.

• 대한수학회논문집
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• 제26권3호
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• pp.483-498
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• 2011

In this paper, we introduce a new class of uniformly point-wise R-subweakly commuting self-mappings and prove several common fixed point theorems and best approximation results for uniformly point-wise R-subweakly commuting asymptotically I-nonexpansive mappings in normed linear spaces. We also establish some results concerning strong convergence of nearest common fixed points of asymptotically I-non-expansive mappings in reflexive Banach spaces with a uniformly G$\^{a}$teaux differentiable norm. Our results unify and generalize various known results given by some authors to a more general class of noncommuting mappings.

• 대한수학회지
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• 제38권6호
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• pp.1245-1260
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• 2001

A demi-closed theorem and some new weak convergence theorems of iterative sequences for asymptotically nonexpansive and nonexpansive mappings in Banach spaces are obtained. The results presented in this paper improve and extend the corresponding results of [1],[8]-[10],[12],[13],[15],[16], and [18].

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.621-633
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• 2014

In this paper, we introduce a general iterative algorithm for asymptotically quasi-${\phi}$-nonexpansive mappings in the intermediate sense to have the strong convergence in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.81-89
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• 2007

In this paper, we introduce the concept of a system of asymptotically quasinonexpansive type mappings. Furthermore, we define a $k$-step iterative sequence approximating common fixed point for a system of asymptotically quasi-nonexpansive type mappings and study its stability in real Banach spaces.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.325-336
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• 2008

In this paper, we prove the weak and strong convergence of the three-step iterative scheme with errors 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.