Several iterative algorithms for solving the split common fixed point problem of directed operators with applications

Optimization ◽  
2014 ◽  
Vol 65 (1) ◽  
pp. 53-65 ◽  
Author(s):  
Yu-Chao Tang ◽  
Li-Wei Liu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

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.

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.

scholarly journals A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 372
Author(s):  
Nishu Gupta ◽  
Mihai Postolache ◽  
Ashish Nandal ◽  
Renu Chugh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Prior Knowledge ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Null Point ◽  
Operator Norm ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

Sign in / Sign up

Export Citation Format

Share Document