Convergence theorems of implicit iterative sequences for a finite family of asymptotically quasi-nonexpansive type mappings

Kim, Jong Kyu; Nam, Young Man; Sim, Jae Yull

doi:10.1016/j.na.2009.06.090

Cited by 21 publications

(8 citation statements)

References 16 publications

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“…We obtain some convergence theorems of common fixed points in the framework of Hilbert spaces. The results presented in this paper mainly improve the corresponding results in Khan et al [9], Kim et al [11], Lv [14], Wang [26] and Zhou [27].…”

Section: Preliminariessupporting

confidence: 86%

“…Implicit iterative algorithms, which are complementary algorithms to the explicit iterative algorithms, have been extensively investigated for fixed points of asymptotically nonexpansive mappings and their extensions; see [8,11,16,17], and the references therein. In this paper, we study the class of asymptotically pseudocontractive nonself-mapping in the intermediate sense based on a one step implicit iterative algorithm.…”

Section: Preliminariesmentioning

confidence: 99%

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Demiclosed principals and convergence theorems for asymptotically pseudocontractive nonself-mappings in intermediate sense

Zhang¹

2017

J. Nonlinear Sci. Appl.

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Section: Preliminariessupporting

confidence: 86%

Section: Preliminariesmentioning

confidence: 99%

Demiclosed principals and convergence theorems for asymptotically pseudocontractive nonself-mappings in intermediate sense

Zhang¹

2017

J. Nonlinear Sci. Appl.

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“…In the framework of Hilbert spaces, (asymptotically) quasi-j-nonexpansive mappings is reduced to (asymptotically) quasi-nonexpansive mappings (cf. [29][30][31][32]). …”

Section: Then P Ep(f) If and Only If P Is A Solution Of The Followingmentioning

confidence: 99%

Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings

Kim

2011

Fixed Point Theory Appl

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We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-j-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25

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“…We denote the set of fixed point of T by F(T ), that is, F(T ) = {x ∈ C : T x = x}. There are many iterative methods for solving a fixed point problem corresponding to an asymptotically nonexpansive mapping (see also [2,12,15,16]). …”

Section: Preliminariesmentioning

confidence: 99%

Cloud hybrid methods for solving split equilibrium and fixed point problems for a family of countable quasi-Lipschitz mappings and applications

Xu¹,

Tang²,

Guan³

et al. 2017

J. Nonlinear Sci. Appl.

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The purpose of this article is to introduce a new multidirectional hybrid shrinking projection iterative algorithm (or called cloud hybrid shrinking projection iterative algorithm) for solving the common element problems which consist of a generalized split equilibrium problems and fixed point problems for a family of countable quasi-Lipschitz mappings in the framework of Hilbert spaces. It is proved that under appropriate conditions, the sequence generated by the multidirectional hybrid shrinking projection method, converges strongly to some point which is the common fixed point of a family of countable quasi-Lipschitz mappings and the solution of the generalized split equilibrium problems. This iteration algorithm can accelerate the convergence speed of iterative sequence. The main results were also applied to solve split variational inequality problem and split optimization problems. Meanwhile, the main results were also used for solving common problems which consist of a generalized split equilibrium problems and fixed point problems for asymptotically nonexpansive mappings. The results of this paper improve and extend the previous results given in the literature.

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Convergence theorems of implicit iterative sequences for a finite family of asymptotically quasi-nonexpansive type mappings

Cited by 21 publications

References 16 publications

Demiclosed principals and convergence theorems for asymptotically pseudocontractive nonself-mappings in intermediate sense

Demiclosed principals and convergence theorems for asymptotically pseudocontractive nonself-mappings in intermediate sense

Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings

Cloud hybrid methods for solving split equilibrium and fixed point problems for a family of countable quasi-Lipschitz mappings and applications

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