scholarly journals Mixed Simultaneous Iterative Algorithms for the Extended Multiple-Set Split Equality Common Fixed-Point Problem with Lipschitz Quasi-Pseudocontractive Operators

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Meixia Li ◽  
Xueling Zhou ◽  
Haitao Che
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Numerical Results ◽  
Point Problem ◽  
Nonexpansive Operator ◽  
Common Fixed Point Problem ◽  
Operator Norms ◽  
Priori Information

In this paper, we study a kind of extended multiple-set split equality common fixed-point problem with Lipschitz quasi-pseudocontractive operators, which is an extension of multiple-set split equality common fixed-point problem with quasi-nonexpansive operator. We propose two mixed simultaneous iterative algorithms, in which the selecting of the stepsize does not need any priori information about the operator norms. Furthermore, we prove that the sequences generated by the mixed simultaneous iterative algorithms converge weakly to the solution of this problem. Some numerical results are shown to illustrate the feasibility and efficiency of the proposed algorithms.

scholarly journals Iterative Algorithms for the Split Problem and Its Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhangsong Yao ◽  
Arif Rafiq ◽  
Shin Min Kang ◽  
Li-Jun Zhu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithms ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Convergence Result ◽  
Feasibility Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

Now, it is known that the split common fixed point problem is a generalization of the split feasibility problem and of the convex feasibility problem. In this paper, the split common fixed point problem associated with the pseudocontractions is studied. An iterative algorithm has been presented for solving the split common fixed point problem. Strong convergence result is obtained.

scholarly journals Strong Convergence Theorems of Viscosity Iterative Algorithms for Split Common Fixed Point Problems

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 14 ◽  
Author(s):  
Peichao Duan ◽  
Xubang Zheng ◽  
Jing Zhao
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Bounded Perturbation ◽  
Common Fixed Point Problem ◽  
Bounded Perturbation Resilience ◽  
Perturbation Resilience ◽  
Split Common Fixed Point

In this paper, we propose a viscosity approximation method to solve the split common fixed point problem and consider the bounded perturbation resilience of the proposed method in general Hilbert spaces. Under some mild conditions, we prove that our algorithms strongly converge to a solution of the split common fixed point problem, which is also the unique solution of the variational inequality problem. Finally, we show the convergence and effectiveness of the algorithms by two numerical examples.

Solving the general split common fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operator norms

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 559-573 ◽  
Author(s):  
Jing Zhao ◽  
Songnian He
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Linear Operators ◽  
Point Problem ◽  
Bounded Linear ◽  
Common Fixed Point Problem ◽  
Operator Norms ◽  
Split Common Fixed Point

Let H1, H2, H3 be real Hilbert spaces, let A : H1 ? H3, B : H2 ? H3 be two bounded linear operators. The general multiple-set split common fixed-point problem under consideration in this paper is to find x ??p,i=1F(Ui), y ??r,j=1 F(Tj) such that Ax = Bym, (1) where p, r ? 1 are integers, Ui : H1 ? H1 (1 ? i ? p) and Tj : H2 ? H2 (1 ? j ? r) are quasi-nonexpansive mappings with nonempty common fixed-point sets ?p,i=1 F(Ui) = ?p,i=1 {x ? H1 : Uix = x} and ?r,j=1F(Tj) = ?r,j=1 {x ? H2 : Tjx = x}. Note that, the above problem (1) allows asymmetric and partial relations between the variables x and y. If H2 = H3 and B = I, then the general multiple-set split common fixed-point problem (1) reduces to the multiple-set split common fixed-point problem proposed by Censor and Segal [J. Convex Anal. 16(2009), 587-600]. In this paper, we introduce simultaneous parallel and cyclic algorithms for the general split common fixed-point problems (1). We introduce a way of selecting the stepsizes such that the implementation of our algorithms does not need any prior information about the operator norms. We prove the weak convergence of the proposed algorithms and apply the proposed algorithms to the multiple-set split feasibility problems. Our results improve and extend the corresponding results announced by many others.

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