Strong Convergence for the Split Common Fixed-Point Problem for Total Quasi-Asymptotically Nonexpansive Mappings in Hilbert Space

Mohammed, Lawan Bulama; Kılıçman, Adem

doi:10.1155/2015/412318

Cited by 7 publications

(7 citation statements)

References 10 publications

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“…Abstract and Applied Analysis 7 Remark 12. Algorithm (7) and Theorems 10 and 11 improve and extend the corresponding results of Censor and Segal [2], Moudafi [3,4], Mohammed [5,6], Chang et al [11,13], Yang et al [12], and others.…”

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confidence: 73%

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Strong Convergence Algorithms of the Split Common Fixed Point Problem for Total Quasi-Asymptotically Pseudocontractive Operators

Wang

Zhou

2014

Abstract and Applied Analysis

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We present a new algorithm for solving the two-set split common fixed point problem with total quasi-asymptotically pseudocontractive operators and consider the case of quasi-pseudocontractive operators. Under some appropriate conditions, we prove that the proposed algorithms have strong convergence. The results presented in this paper improve and extend the previous algorithms and results of Censor and Segal (2009), Moudafi (2011 and 2010), Mohammed (2013), Yang et al. (2011), Chang et al. (2012), and others.

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supporting

confidence: 73%

“…Moudafi's results are weak convergence. In [5,6], Mohammed utilized the strongly quasi-nonexpansive operators and quasi-nonexpansive operators to solve recursion (5) and obtain weak and strong convergence, respectively. Strong convergence of (5) with pseudo-demicontractive and firmly pseudo-demicontractive mappings can be found in [7,8].…”

Section: Introductionmentioning

confidence: 99%

Strong Convergence Algorithms of the Split Common Fixed Point Problem for Total Quasi-Asymptotically Pseudocontractive Operators

Wang

Zhou

2014

Abstract and Applied Analysis

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“…Lemma 2.50. (Mohammed and Kilicman [86]) Let P C : H → C be a metric projection such that x n − x * , x n − P C x n ≤ 0. Then for each n ≥ 1,…”

Section: Preliminary Resultsmentioning

confidence: 99%

A Note on the Split Common Fixed Point Problem and its Variant Forms

Kılıçman

Mohammed

2018

Mathematical Analysis and Applications

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The split common fixed point problems has found its applications in various branches of mathematics both pure and applied. It provides us a unified structure to study a large number of nonlinear mappings. Our interest here is to apply these mappings and propose some iterative methods for solving the split common fixed point problems and its variant forms, and we prove the convergence results of these algorithms.As a special case of the split common fixed problems, we consider the split common fixed point equality problems for the class of finite family of quasinonexpansive mappings. Furthermore, we consider another problem namely split feasibility and fixed point equality problems and suggest some new iterative methods and prove their convergence results for the class of quasinonexpansive mappings.Finally, as a special case of the split feasibility and fixed point equality problems, we consider the split feasibility and fixed point problems and propose Ishikawa-type extra-gradients algorithms for solving these split feasibility and fixed point problems for the class of quasi-nonexpansive mappings in Hilbert spaces. In the end, we prove the convergence results of the proposed algorithms.Results proved in this chapter continue to hold for different type of problems, such as; convex feasibility problem, split feasibility problem and multipleset split feasibility problems.

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“…Lemma 1 [7] let be a nonempty closed convex subset of Hilbert space and be a metric projection from onto satisfying then Then converges strongly to Proof: To show that it suffices to show and . We divided the proof into four steps as follows.…”

Section: Preliminariesmentioning

confidence: 99%

Strong convergence for the split common fixed point problems for demicontractive mappings in Hilbert spaces

Kılıçman¹,

Mohammed²

2016

AIP Conference Proceedings

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Abstract. The split common fixed problem (SCFPP) has been intensively studied by numerous author due to its various applications in many physical problem. However, to employ the algorithm for solving such a problem, one needs to know the prior information on the normed of bounded linear operator. Recently, Cui and Wang introduced the new algorithm for solving such a problem which does not needs any prior information on the normed on bounded linear operator and they established the weak convergence results under some mild conditions. It is well-known that in setting of infinite dimensional Hilbert space, the weak convergence does not implies strong convergence. It is the aims of this article to continue studying this problem (SCFPP) and establish the strong convergence result based on the result of Cui and Wang, this will be done for the class of demicontractive mappings. The results presented in this paper, not only extend and improve the result of Cui and Wang, but also extend, improve and generalize several well-known results announced.

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Strong Convergence for the Split Common Fixed-Point Problem for Total Quasi-Asymptotically Nonexpansive Mappings in Hilbert Space

Cited by 7 publications

References 10 publications

Strong Convergence Algorithms of the Split Common Fixed Point Problem for Total Quasi-Asymptotically Pseudocontractive Operators

Strong Convergence Algorithms of the Split Common Fixed Point Problem for Total Quasi-Asymptotically Pseudocontractive Operators

A Note on the Split Common Fixed Point Problem and its Variant Forms

Strong convergence for the split common fixed point problems for demicontractive mappings in Hilbert spaces

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