Another look at Wang’s new method for solving split common fixed-point problems without priori knowledge of operator norms

2018 ◽  
Vol 20 (2) ◽  
Author(s):  
Rapeepan Kraikaew ◽  
Satit Saejung
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Problems ◽  
New Method ◽  
Operator Norms ◽  
Split Common Fixed Point ◽  
Priori Knowledge

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 On split common fixed point problems

2014 ◽  
Vol 415 (2) ◽  
pp. 513-524 ◽  
Author(s):  
Rapeepan Kraikaew ◽  
Satit Saejung
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Problems ◽  
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.

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