• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.107-121
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• 2013

The purpose of this paper is to investigate the demiclosed principle, the existence theorems and convergence theorems in CAT(0) spaces for a class of mappings which is essentially wider than that of asymptotically nonexpansive mappings. The structure of fixed point set of such mappings is also studied. Our results generalize, unify and extend several comparable results in the existing literature.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.665-678
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• 2019

We construct an iteration scheme involving a hybrid pair of mappings, one a single-valued asymptotically nonexpansive mapping t and the other a multivalued nonexpansive mapping T, in a complete CAT(0) space. In the process, we remove a restricted condition (called the end-point condition) from results of Akkasriworn and Sokhuma [1] and and use this to prove some convergence theorems. The results concur with analogues for Banach spaces from Uddin et al. [16].

• 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.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.39-46
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• 2017

In this paper, we propose a new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex cone metric spaces. Then we show that our iteration converges to a common fixed point of this class of mappings under suitable conditions. Our result generalizes the corresponding result of Lee [5] from the closed convex subset of a convex cone metric space to whole space.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.455-469
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• 2002

The Purpose Of this Paper is to introduce the concept of a class of strictly successively hemicontractive mappings and construct certain stable and almost stable iteration procedures for the iterative approximation of fixed points for asymptotically nonexpansive and strictly successively hemicontractive mappings in Banach spaces.

• East Asian mathematical journal
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• v.27 no.1
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• pp.35-49
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• 2011

In this paper, we study multi-step iterative algorithm with errors and give the necessary and sufficient condition to converge to com mon fixed points for a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces. Also we have proved a strong convergence theorem to converge to common fixed points for a finite family said mappings on a nonempty compact convex subset of a uniformly convex Banach spaces. Our results extend and improve the corresponding results of [2, 4, 7, 8, 9, 10, 12, 15, 20].

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.313-321
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• 2017

In this note we establish a new non-convex hybrid iteration algorithm corresponding to Khan iterative process [4] and prove strong convergence theorems of common fixed points for a uniformly closed asymptotically family of countable quasi-Lipschitz mappings in Hilbert spaces. Moreover, the main results are applied to get the common fixed points of finite family of quasi-asymptotically nonexpansive mappings. The results presented in this article are interesting extensions of some current results.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.29-40
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• 2008

In this paper, we introduce a modified three-step iteration scheme with errors for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. We then use this scheme to approximate a common fixed point of these mappings. The results obtained in this paper extend and improve the recent ones announced by Khan, Fukhar-ud-di, Zhou, Cho, Noor and some others.

• East Asian mathematical journal
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• v.28 no.5
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• pp.617-630
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• 2012

In this paper, the problem of iterative approximation of common fixed points of asymptotically nonexpansive is investigated in the framework of Banach spaces. Weak convergence theorems are established. A necessary and sufficient condition for strong convergence is also discussed. As an application of main results, a variational inequality is investigated.

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.111-115
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• 2003

Under some asymptotical conditions we obtain a fixed point theorem for a mapping(not necessarily nonexpansive) from an unbounded closed convex subset of a reflexive Banach space into itself. Also we give an example for applying it.