scholarly journals Weak convergence of a primal-dual algorithm for split common fixed-point problems in Hilbert spaces

2020 ◽  
Vol 2 (2) ◽  
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Dual Algorithm ◽  
Primal Dual ◽  
Split Common Fixed Point

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 Viscosity Methods and Split Common Fixed Point Problems for Demicontractive Mappings

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 844 ◽  
Author(s):  
Yaqin Wang ◽  
Xiaoli Fang ◽  
Tae-Hwa Kim
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
A Priori ◽  
Fixed Point Problems ◽  
A Priori Knowledge ◽  
Type Algorithm ◽  
Operator Norms ◽  
Demicontractive Mappings ◽  
Split Common Fixed Point

We, first, propose a new method for solving split common fixed point problems for demicontractive mappings in Hilbert spaces, and then establish the strong convergence of such an algorithm, which extends the Halpern type algorithm studied by Wang and Xu to a viscosity iteration. Above all, the step sizes in this algorithm are chosen without a priori knowledge of the operator norms.

scholarly journals Multiple-Sets Split Common Fixed-Point Problems for Demicontractive Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Huanhuan Cui
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Common Fixed Point ◽  
Iterative Methods ◽  
Fixed Point Problems ◽  
Mild Conditions ◽  
Demicontractive Mappings ◽  
Split Common Fixed Point

In this paper, we are concerned with the multiple-sets split common fixed-point problems whenever the involved mappings are demicontractive. We first study several properties of demicontractive mappings and particularly their connection with directed mappings. By making use of these properties, we propose some new iterative methods for solving multiple-sets split common fixed-point problems, as well as multiple-sets spit feasibility problems. Under mild conditions, we establish their weak convergence of the proposed methods.

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