scholarly journals Strong convergence for the split common fixed point problems for demicontractive mappings in Hilbert spaces

2016 ◽  
Author(s):  
A. Kilicman ◽  
L. B. Mohammed
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Demicontractive Mappings ◽  
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.

Solving split equality common fixed point problem for infinite families of demicontractive mappings

2018 ◽  
Vol 34 (3) ◽  
pp. 321-331
Author(s):  
ADISAK HANJING ◽  
◽  
SUTHEP SUANTAI ◽  
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Demicontractive Mappings

In this paper, we consider the split equality common fixed point problem of infinite families of demicontractive mappings in Hilbert spaces. We introduce a simultaneous iterative algorithm for solving the split equality common fixed point problem of infinite families of demicontractive mappings and prove a strong convergence of the proposed algorithm under some control conditions.

scholarly journals On the Strong Convergence of an Algorithm about Firmly Pseudo-Demicontractive Mappings for the Split Common Fixed-Point Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yanrong Yu ◽  
Delei Sheng
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Demicontractive Mappings ◽  
Split Common Fixed Point ◽  
Modified Algorithm

Based on the recent work by Censor and Segal (2009 J. Convex Anal.16), and inspired by Moudafi (2010 Inverse Problems 26), we modify the algorithm of demicontractive operators proposed by Moudafi and study the modified algorithm for the class of firmly pseudodemicontractive operators to solve the split common fixed-point problem in a Hilbert space. We also give the strong convergence theorem under some appropriate conditions. Our work improves and/or develops the work of Moudafi, Censor and Segal, and other results.

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