scholarly journals Two methods for solving split common fixed point problems of strict pseudo-contractve mappings in Hilbert spaces with applications

2021 ◽  
Vol 3 (1) ◽  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Split Common Fixed Point

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 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.

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