scholarly journals Improved self-adaptive iterative algorithms for the split equality common fixed-point problem of firmly quasi-nonexpansive operators

2020 ◽  
Vol 2020 (1) ◽  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Nonexpansive Operators ◽  
Self Adaptive

scholarly journals A new self-adaptive accelerated method for generalized split system of common fixed-point problem of averaged mappings

2021 ◽  
Author(s):  
Anteneh Getachew Gebrie ◽  
Dejene Shewakena Bedane
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Weak Convergence Theorem ◽  
Theoretical Application ◽  
Averaged Mappings ◽  
Split System ◽  
Self Adaptive

AbstractThe purpose of this paper is to propose a new inertial self-adaptive algorithm for generalized split system of common fixed point problems of finite family of averaged mappings in the framework of Hilbert spaces. The weak convergence theorem of the proposed method is given and its theoretical application for solving several generalized problems is presented. The behavior and efficiency of the proposed algorithm is illustrated by some numerical tests.

scholarly journals Iterative Algorithms for the Split Problem and Its Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhangsong Yao ◽  
Arif Rafiq ◽  
Shin Min Kang ◽  
Li-Jun Zhu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithms ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Convergence Result ◽  
Feasibility Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

Now, it is known that the split common fixed point problem is a generalization of the split feasibility problem and of the convex feasibility problem. In this paper, the split common fixed point problem associated with the pseudocontractions is studied. An iterative algorithm has been presented for solving the split common fixed point problem. Strong convergence result is obtained.

scholarly journals Strong Convergence Theorems of Viscosity Iterative Algorithms for Split Common Fixed Point Problems

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 14 ◽  
Author(s):  
Peichao Duan ◽  
Xubang Zheng ◽  
Jing Zhao
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Bounded Perturbation ◽  
Common Fixed Point Problem ◽  
Bounded Perturbation Resilience ◽  
Perturbation Resilience ◽  
Split Common Fixed Point

In this paper, we propose a viscosity approximation method to solve the split common fixed point problem and consider the bounded perturbation resilience of the proposed method in general Hilbert spaces. Under some mild conditions, we prove that our algorithms strongly converge to a solution of the split common fixed point problem, which is also the unique solution of the variational inequality problem. Finally, we show the convergence and effectiveness of the algorithms by two numerical examples.

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