Regularization Methods for Nonexpansive Semigroups in Hilbert Spaces

2015 ◽  
Vol 44 (3) ◽  
pp. 637-648
Author(s):  
Pham Thanh Hieu ◽  
Nguyen Thi Thu Thuy
Keyword(s):  
Hilbert Spaces ◽  
Regularization Methods ◽  
Nonexpansive Semigroups

scholarly journals Approximation of fixed points for nonexpansive semigroups in Hilbert spaces

2013 ◽  
Vol 2013 (1) ◽  
pp. 31 ◽  
Author(s):  
Yonghong Yao ◽  
Jung Kang ◽  
Yeol Cho ◽  
Yeong-Cheng Liou
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Semigroups

scholarly journals On fractional asymptotical regularization of linear ill-posed problems in hilbert spaces

2019 ◽  
Vol 22 (3) ◽  
pp. 699-721 ◽  
Author(s):  
Ye Zhang ◽  
Bernd Hofmann
Keyword(s):  
Fractional Order ◽  
Hilbert Spaces ◽  
Regularization Method ◽  
Numerical Realization ◽  
Regularization Methods ◽  
Iterative Regularization ◽  
Operator Equations ◽  
Ill Posed ◽  
One Step ◽  
The One

Abstract In this paper, we study a fractional-order variant of the asymptotical regularization method, called Fractional Asymptotical Regularization (FAR), for solving linear ill-posed operator equations in a Hilbert space setting. We assign the method to the general linear regularization schema and prove that under certain smoothness assumptions, FAR with fractional order in the range (1, 2) yields an acceleration with respect to comparable order optimal regularization methods. Based on the one-step Adams-Moulton method, a novel iterative regularization scheme is developed for the numerical realization of FAR. Two numerical examples are given to show the accuracy and the acceleration effect of FAR.

Strong and weak convergence theorems for general mixed equilibrium problems and general variational inequality problems and fixed point problems for two nonexpansive semigroups in Hilbert spaces

2021 ◽  
pp. 152-160
Author(s):  
Baoshuai Zhang ◽  
◽  
Ying Tian ◽  
Keyword(s):  
Variational Inequality ◽  
Weak Convergence ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Common Element ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Nonexpansive Semigroups ◽  
General Variational Inequality ◽  
Mixed Equilibrium

In this paper, we introduce some iterative algorithms for finding a common element of the set of solutions of the general mixed equilibrium problem and the set of solutions of a general variational inequality for two cocoercive mappings and the set of common fixed points of two nonexpansive semigroups in Hilbert space. We obtain both strong and weak convergence theorems for the sequences generated by these iterative processes in Hilbert spaces. Our results improve and extend the results announced by many others.

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