A new method for split common fixed-point problem without priori knowledge of operator norms

2017 ◽  
Vol 19 (4) ◽  
pp. 2427-2436 ◽  
Author(s):  
Fenghui Wang
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
New Method ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Operator Norms ◽  
Split Common Fixed Point ◽  
Priori Knowledge

scholarly journals Weak Convergence Theorems on the Split Common Fixed Point Problem for Demicontractive Continuous Mappings

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Huanhuan Cui ◽  
Luchuan Ceng ◽  
Fenghui Wang
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
New Method ◽  
Point Problem ◽  
Lipschitz Continuous ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

We are concerned with the split common fixed point problem in Hilbert spaces. We propose a new method for solving this problem and establish a weak convergence theorem whenever the involved mappings are demicontractive and Lipschitz continuous. As an application, we also obtain a new method for solving the split equality problem in Hilbert spaces.

Solving the general split common fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operator norms

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 559-573 ◽  
Author(s):  
Jing Zhao ◽  
Songnian He
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Linear Operators ◽  
Point Problem ◽  
Bounded Linear ◽  
Common Fixed Point Problem ◽  
Operator Norms ◽  
Split Common Fixed Point

Let H1, H2, H3 be real Hilbert spaces, let A : H1 ? H3, B : H2 ? H3 be two bounded linear operators. The general multiple-set split common fixed-point problem under consideration in this paper is to find x ??p,i=1F(Ui), y ??r,j=1 F(Tj) such that Ax = Bym, (1) where p, r ? 1 are integers, Ui : H1 ? H1 (1 ? i ? p) and Tj : H2 ? H2 (1 ? j ? r) are quasi-nonexpansive mappings with nonempty common fixed-point sets ?p,i=1 F(Ui) = ?p,i=1 {x ? H1 : Uix = x} and ?r,j=1F(Tj) = ?r,j=1 {x ? H2 : Tjx = x}. Note that, the above problem (1) allows asymmetric and partial relations between the variables x and y. If H2 = H3 and B = I, then the general multiple-set split common fixed-point problem (1) reduces to the multiple-set split common fixed-point problem proposed by Censor and Segal [J. Convex Anal. 16(2009), 587-600]. In this paper, we introduce simultaneous parallel and cyclic algorithms for the general split common fixed-point problems (1). We introduce a way of selecting the stepsizes such that the implementation of our algorithms does not need any prior information about the operator norms. We prove the weak convergence of the proposed algorithms and apply the proposed algorithms to the multiple-set split feasibility problems. Our results improve and extend the corresponding results announced by many others.

scholarly journals Adaptive algorithm for solving the SCFPP of demicontractive operators without a priori knowledge of operator norms

2019 ◽  
Vol 27 (3) ◽  
pp. 153-175 ◽  
Author(s):  
Duangkamon Kitkuan ◽  
Poom Kumam ◽  
Vasile Berinde ◽  
Anantachai Padcharoen
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
A Priori ◽  
Fixed Point Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Common Solution ◽  
Common Fixed Point Problem ◽  
Operator Norms ◽  
Split Common Fixed Point

AbstractIn this paper, we study the split common fixed point problem in Hilbert spaces. We find a common solution of the split common fixed point problem for two demicontractive operators without a priori knowledge of operator norms. A strong convergence theorem is obtained under some additional conditions and numerical examples are included to illustrate the applications in signal compressed sensing and image restoration.

scholarly journals A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 372
Author(s):  
Nishu Gupta ◽  
Mihai Postolache ◽  
Ashish Nandal ◽  
Renu Chugh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Prior Knowledge ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Null Point ◽  
Operator Norm ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

Generalized self-adaptive algorithm for solving split common fixed point problem and its application to image restoration problem

2019 ◽  
Vol 97 (7) ◽  
pp. 1431-1443 ◽  
Author(s):  
Raweerote Suparatulatorn ◽  
Anchalee Khemphet ◽  
Phakdi Charoensawan ◽  
Suthep Suantai ◽  
Narawadee Phudolsitthiphat
Keyword(s):  
Fixed Point ◽  
Image Restoration ◽  
Common Fixed Point ◽  
Adaptive Algorithm ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point ◽  
Restoration Problem ◽  
Self Adaptive
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