• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.801-812
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• 2010

In this paper, we consider the convergence of the shrinking projection method for quasi-$\phi$-nonexpansive mappings. Strong convergence theorems are established in a uniformly smooth and strictly convex Banach space which enjoys the Kadec-Klee property.

• 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.

• 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.24 no.4
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• pp.539-551
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• 2009

In this paper, we propose a modified hybrid algorithm and prove strong convergence theorems for a family of quasi-$\phi$-asymptotically nonexpansive mappings. Our results extend and improve the results by Nakajo, Takahashi, Kim, Xu, Su and some others.

• 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.

• East Asian mathematical journal
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• v.27 no.1
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• pp.1-9
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• 2011

In this paper, we consider an iterative scheme for finding a common element of the set of fixed points of a asymptotically quasi nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common fixed point of a asymptotically quasi-nonexpansive mapping and strictly pseudocontractive mapping and the problem of finding a common element of the set of fixed points of a asymptotically quasi-nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.73-82
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• 2010

In an infinite-dimensional Hilbert space, the normal Mann iteration has only weak convergence, in general, even for nonexpansive mappings. The purpose of this paper is to modify the normal Mann iteration to have strong convergence for a closed quasi-$\phi$-nonexpansive mapping in the framework of Banach spaces.

• Kyungpook Mathematical Journal
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• v.47 no.1
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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.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.703-723
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• 2019

In this paper, we consider a common solution of three problems in real Hilbert spaces: the Ky Fan inequality problem, the variational inequality problem and the fixed point problem for demicontractive single-valued and quasi-nonexpansive multi-valued mappings. To find the solution we present a new iterative algorithm and prove a strong convergence theorem under mild conditions. Moreover, we provide a numerical example to illustrate the convergence behavior of the proposed iterative method.

• 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.