The split common fixed point problem for infinite families of total quasi-asymptotically nonexpansive operators

2013 ◽  
Vol 67 (2) ◽  
pp. 243-256
Author(s):  
Wei-Qi Deng
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Asymptotically Nonexpansive ◽  
Nonexpansive Operators ◽  
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 Strong Convergence Theorems for Split Common Fixed Point Problem of Bregman Generalized Asymptotically Nonexpansive Mappings in Banach Spaces

2019 ◽  
pp. 35-50
Author(s):  
Yusuf Ibrahim
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Asymptotically Nonexpansive ◽  
Split Common Fixed Point

In this paper, a new iterative scheme is introduced and also strong convergence theorems for solving split common fixed point problem for uniformly continuous Bregman generalized asymptotically nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces are presented. The results are proved without the assumption of semicompactness property and or Opial condition

scholarly journals Strong Convergence for the Split Common Fixed-Point Problem for Total Quasi-Asymptotically Nonexpansive Mappings in Hilbert Space

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Lawan Bulama Mohammed ◽  
A. Kılıçman
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Asymptotically Nonexpansive ◽  
Split Common Fixed Point

In this paper, we study and modify the algorithm of Kraikaew and Saejung for the class of total quasi-asymptotically nonexpansive case so that the strong convergence is guaranteed for the solution of split common fixed-point problems in Hilbert space. Moreover, we justify our result through an example. The results presented in this paper not only extend the result of Kraikaew and Saejung but also extend, improve, and generalize some existing results in the literature.

scholarly journals Inertial Iteration for Split Common Fixed-Point Problem for Quasi-Nonexpansive Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yazheng Dang ◽  
Yan Gao
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Recent Work ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Nonexpansive Operators ◽  
Split Common Fixed Point ◽  
Asymptotical Convergence

Inspired by the note on split common fixed-point problem for quasi-nonexpansive operators presented by Moudafi (2011), based on the very recent work by Dang et al. (2012), in this paper, we propose an inertial iterative algorithm for solving the split common fixed-point problem for quasi-nonexpansive operators in the Hilbert space. We also prove the asymptotical convergence of the algorithm under some suitable conditions. The results improve and develop previously discussed feasibility problems and related algorithms.

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