A simultaneous iterative method for split equality problems of two finitefamilies of strictly pseudononspreading mappings without prior knowledge ofoperator norms

Che, Haitao; Li, Meixia

doi:10.1186/1687-1812-2015-1

Cited by 52 publications

(15 citation statements)

References 16 publications

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“…In 2015, Che and Li [10] proposed the following iterative algorithm for finding a solution of (SEFPP) (1.4): 6) and proved the weak convergence of the scheme (1.6) under the condition that the operators T and S are quasi-nonexpansive mappings.…”

Section: Introductionmentioning

confidence: 99%

Hybrid projection algorithm concerning split equality fixed point problem for quasi-pseudo-contractive mappings with application to optimization problem

Tang¹,

Chang²,

Wen³

et al. 2016

J. Nonlinear Sci. Appl.

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The purpose of this paper is by using the shrinking projection method to study the split equality fixed point problem for a class of quasi-pseudo-contractive mappings in the setting of Hilbert spaces. Under suitable conditions, some strong convergence theorems are obtained. As applications, we utilize the results presented in the paper to study the existence problem of solutions to the split equality variational inequality problem and the split equality convex minimization problem. The results presented in our paper extend and improve some recent results. c 2016 all rights reserved.Keywords: Split equality fixed point problem, quasi-pseudo-contractive mapping, hybrid projection algorithm, strong convergence theorem. 2010 MSC: 47J20, 47H10, 49J25.

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Section: Introductionmentioning

confidence: 99%

Hybrid projection algorithm concerning split equality fixed point problem for quasi-pseudo-contractive mappings with application to optimization problem

Tang¹,

Chang²,

Wen³

et al. 2016

J. Nonlinear Sci. Appl.

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“…The split equality problem (SEP ) and split equality fixed point problem (SEF P P ) have been studied by many authors [9][10][11][12][13][14][15][16][17]. To solve the (SEF P P ), Modaufi [9] presented the following simultaneous iterative method and obtained weak convergence theorem:…”

Section: 3)mentioning

confidence: 99%

The strong convergence theorems for the split equality fixed point problems in Hilbert spaces

Niu¹,

Zhou²,

Zhang³

et al. 2018

ams

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“…Recently, many results on split equality fixed point problem have been found and one is referred to [8,10,23,24,26,27] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous iteration for variational inequalities over common solutions for finite families of nonlinear problems

Lin¹

2018

J. Nonlinear Sci. Appl.

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In this paper, we apply Theorem 3.2 of [G. M. Lee, L.-J. Lin, J. Nonlinear Convex Anal., 18 (2017), 1781-1800] to study the variational inequality over split equality fixed point problems for three finite families of strongly quasi-nonexpansive mappings. Then we use this result to study variational inequalities over split equality for three various finite families of nonlinear mappings. We give a unified method to study split equality for three various finite families of nonlinear problems. Our results contain many results on split equality fixed point problems and multiple sets split feasibility problems as special cases. Our results can treat large scale of nonlinear problems by group these problems into finite families of nonlinear problems, then we use simultaneous iteration to find the solutions of these problems. Our results will give a simple and quick method to study large scale of nonlinear problems and will have many applications to study large scale of nonlinear problems.Keywords: Split equality fixed point problem, split fixed point problem, quasi-pseudocontractive mapping, demicontractive mapping, pseudo-contractive mapping.

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A simultaneous iterative method for split equality problems of two finitefamilies of strictly pseudononspreading mappings without prior knowledge ofoperator norms

Cited by 52 publications

References 16 publications

Hybrid projection algorithm concerning split equality fixed point problem for quasi-pseudo-contractive mappings with application to optimization problem

Hybrid projection algorithm concerning split equality fixed point problem for quasi-pseudo-contractive mappings with application to optimization problem

The strong convergence theorems for the split equality fixed point problems in Hilbert spaces

Simultaneous iteration for variational inequalities over common solutions for finite families of nonlinear problems

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