Parallel Iterative Methods for Solving the Split Common Fixed Point Problem in Hilbert Spaces

2019 ◽  
Vol 41 (7) ◽  
pp. 778-805
Author(s):  
Simeon Reich ◽  
Truong Minh Tuyen ◽  
Nguyen Minh Trang
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Parallel Iterative Methods ◽  
Common Fixed Point Problem ◽  
Parallel Iterative ◽  
Split Common Fixed Point

scholarly journals The Split Common Fixed Point Problem for Quasi-Total Asymptotically Nonexpansive Uniformly Lipschitzian Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Jing Na ◽  
Lin Wang ◽  
Zhaoli Ma
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Lipschitzian Mappings ◽  
Common Fixed Point Problem ◽  
Asymptotically Nonexpansive ◽  
Uniformly Lipschitzian Mapping ◽  
Split Common Fixed Point

We introduce an algorithm for solving the split common fixed point problem for quasi-total asymptotically nonexpansive uniformly Lipschitzian mapping in Hilbert spaces. The results presented in this paper improve and extend some recent corresponding results.

scholarly journals Weak Convergence Theorems on the Split Common Fixed Point Problem for Demicontractive Continuous Mappings

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Huanhuan Cui ◽  
Luchuan Ceng ◽  
Fenghui Wang
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
New Method ◽  
Point Problem ◽  
Lipschitz Continuous ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

We are concerned with the split common fixed point problem in Hilbert spaces. We propose a new method for solving this problem and establish a weak convergence theorem whenever the involved mappings are demicontractive and Lipschitz continuous. As an application, we also obtain a new method for solving the split equality problem in Hilbert spaces.

scholarly journals An Inertial Method for Split Common Fixed Point Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Haixia Zhang ◽  
Huanhuan Cui
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Linear Mapping ◽  
Point Problem ◽  
Inertial Method ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point ◽  
Inertial Technique

In this paper, we consider the split common fixed point problem in Hilbert spaces. By using the inertial technique, we propose a new algorithm for solving the problem. Under some mild conditions, we establish two weak convergence theorems of the proposed algorithm. Moreover, the stepsize in our algorithm is independent of the norm of the given linear mapping, which can further improve the performance of the algorithm.

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