A new self-adaptive method for the split equality common fixed-point problem of quasi-nonexpansive mappings

Optimization ◽  
2020 ◽  
pp. 1-22
Author(s):  
Jing Zhao ◽  
Dingfang Hou ◽  
Xinglong Wang
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Adaptive Method ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
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 A Strong Convergence Algorithm for the Two-Operator Split Common Fixed Point Problem in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chung-Chien Hong ◽  
Young-Ye Huang
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Intensity Modulated Radiation Therapy ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Numerical Result ◽  
Common Fixed Point Problem ◽  
Operator Split ◽  
Split Common Fixed Point

The two-operator split common fixed point problem (two-operator SCFP) with firmly nonexpansive mappings is investigated in this paper. This problem covers the problems of split feasibility, convex feasibility, and equilibrium and can especially be used to model significant image recovery problems such as the intensity-modulated radiation therapy, computed tomography, and the sensor network. An iterative scheme is presented to approximate the minimum norm solution of the two-operator SCFP problem. The performance of the presented algorithm is compared with that of the last algorithm for the two-operator SCFP and the advantage of the presented algorithm is shown through the numerical result.

scholarly journals Common Fixed-Point Problem for a Family Multivalued Mapping in Banach Space

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Zhanfei Zuo
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Fixed Point Set ◽  
Common Fixed Point Problem ◽  
The Family ◽  
Point Set ◽  
The Common

It is our purpose in this paper to prove two convergents of viscosity approximation scheme to a common fixed point of a family of multivalued nonexpansive mappings in Banach spaces. Moreover, it is the unique solution in to a certain variational inequality, where stands for the common fixed-point set of the family of multivalued nonexpansive mapping .

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 of the Viscosity Approximation Process for the Split Common Fixed-Point Problem of Quasi-Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jing Zhao ◽  
Songnian He
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Viscosity Approximation ◽  
Approximation Process ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

Very recently, Moudafi (2011) introduced an algorithm with weak convergence for the split common fixed-point problem. In this paper, we will continue to consider the split common fixed-point problem. We discuss the strong convergence of the viscosity approximation method for solving the split common fixed-point problem for the class of quasi-nonexpansive mappings in Hilbert spaces. Our results improve and extend the corresponding results announced by many others.

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