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 A CYCLIC ALGORITHM FOR THE SPLIT COMMON FIXED POINT PROBLEM OF DEMICONTRACTIVE MAPPINGS IN HILBERT SPACES

2012 ◽  
Vol 17 (4) ◽  
pp. 457-466 ◽  
Author(s):  
Yu-Chao Tang ◽  
Ji-Gen Peng ◽  
Li-Wei Liu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Cyclic Algorithm ◽  
Demicontractive Mappings ◽  
Split Common Fixed Point

The split common fixed point problem has been investigated recently, which is a generalization of the split feasibility problem and of the convex feasibility problem. We construct a cyclic algorithm to approximate a solution of the split common fixed point problem for the demicontractive mappings in a Hilbert space. Our results improve and extend previously discussed related problems and algorithms.

scholarly journals An alternating iteration algorithm for solving the split equality fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Meixia Li ◽  
Xueling Zhou ◽  
Haitao Che
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Iteration Algorithm ◽  
Point Problem ◽  
Contractive Mappings ◽  
Common Fixed Point Problem ◽  
Significant Generalization

Abstract In this paper, we are concerned with the split equality common fixed point problem. It is a significant generalization of the split feasibility problem, which can be used in various disciplines, such as medicine, military and biology, etc. We propose an alternating iteration algorithm for solving the split equality common fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings and prove that the sequence generated by the algorithm converges weakly to the solution of this problem. Finally, some numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.

scholarly journals Shrinking Projection Methods for Split Common Fixed-Point Problems in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Huan-chun Wu ◽  
Cao-zong Cheng
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Projection Methods ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Split Common Fixed Point

Inspired by Moudafi (2011) and Takahashi et al. (2008), we present the shrinking projection method for the split common fixed-point problem in Hilbert spaces, and we obtain the strong convergence theorem. As a special case, the split feasibility problem is also considered.

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.

scholarly journals Weak and Strong Convergence Theorems for the Multiple-Set Split Equality Common Fixed-Point Problems of Demicontractive Mappings

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Yaqin Wang ◽  
Tae-Hwa Kim ◽  
Xiaoli Fang
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Iterative Algorithms ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Point Problem ◽  
Weak And Strong Convergence ◽  
Demicontractive Mappings

We consider mixed parallel and cyclic iterative algorithms in this paper to solve the multiple-set split equality common fixed-point problem which is a generalization of the split equality problem and the split feasibility problem for the demicontractive mappings without prior knowledge of operator norms in real Hilbert spaces. Some weak and strong convergence results are established. The results obtained in this paper generalize and improve the recent ones announced by many others.

scholarly journals Iterative Algorithms for Split Common Fixed Point Problem Involved in Pseudo-Contractive Operators without Lipschitz Assumption

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 777
Author(s):  
Jinzuo Chen ◽  
Mihai Postolache ◽  
Li-Jun Zhu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Numerical Examples ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

Two iterative algorithms are suggested for approximating a solution of the split common fixed point problem involved in pseudo-contractive operators without Lipschitz assumption. We prove that the sequence generated by the first algorithm converges weakly to a solution of the split common fixed point problem and the second one converges strongly. Moreover, the sequence { x n } generated by Algorithm 3 strongly converges to z = proj S 0 , which is the minimum-norm solution of problem (1). Numerical examples are included.

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