scholarly journals An Inertial Method for Split Common Fixed Point Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Haixia Zhang ◽  
Huanhuan Cui
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Linear Mapping ◽  
Point Problem ◽  
Inertial Method ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point ◽  
Inertial Technique

In this paper, we consider the split common fixed point problem in Hilbert spaces. By using the inertial technique, we propose a new algorithm for solving the problem. Under some mild conditions, we establish two weak convergence theorems of the proposed algorithm. Moreover, the stepsize in our algorithm is independent of the norm of the given linear mapping, which can further improve the performance of the algorithm.

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 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.

scholarly journals A SHRINKING PROJECTION METHOD FOR SOLVING THE SPLIT COMMON FIXED POINT PROBLEM IN HILBERT SPACES

2019 ◽  
Vol 203 (10) ◽  
pp. 31-35
Author(s):  
Mai Thị Ngọc Hà
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Projection Method ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Shrinking Projection Method ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

Trong bài báo này, chúng tôi nghiên cứu bài toán điểm bất động chung tách trong 2 không gian Hilbert. Cho H1 và H2 là hai không gian Hilbert thực. Cho S1: H1 → H1, và S2: H2 → H2, là hai ánh xạ không giãn trên không gian H1và H2 tương ứng. Bài toán đặt ra là: tìm một phần tử x† ∈ H1 sao cho:                                                           x† ∈ Ω := Fix(S1) ∩ T−1( Fix(S2)) ≠ ∅,Khi T : H1 → H2là một ánh xạ tuyến tính bị chặn cho trước từ H1 vào H2. Sử dụng phương pháp chiếu thu hẹp, chúng tôi đề xuất một thuật toán mới (Thuật toán 3.1) để giải bài toán này và thiết lập một định lý hội thụ mạnh cho thuật toán (Định lý 3.3).

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