scholarly journals Strong and weak convergence theorems for a new split feasibility problem

2013 ◽  
Vol 8 ◽  
pp. 1621-1627 ◽  
Author(s):  
Yuan-Fang Ma ◽  
Lin Wang ◽  
Xue-Jiao Zi
Keyword(s):  
Weak Convergence ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Split Feasibility

scholarly journals S-Subgradient Projection Methods with S-Subdifferential Functions for Nonconvex Split Feasibility Problems

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1517
Author(s):  
Jinzuo Chen ◽  
Mihai Postolache ◽  
Yonghong Yao
Keyword(s):  
Weak Convergence ◽  
Projection Method ◽  
Split Feasibility Problem ◽  
Projection Methods ◽  
Feasibility Problem ◽  
Split Feasibility Problems ◽  
Finite Dimensional ◽  
Subgradient Projection ◽  
Weak Convergence Theorem ◽  
Split Feasibility

In this paper, the original C Q algorithm, the relaxed C Q algorithm, the gradient projection method ( G P M ) algorithm, and the subgradient projection method ( S P M ) algorithm for the convex split feasibility problem are reviewed, and a renewed S P M algorithm with S-subdifferential functions to solve nonconvex split feasibility problems in finite dimensional spaces is suggested. The weak convergence theorem is established.

scholarly journals Solving a Split Feasibility Problem by the Strong Convergence of Two Projection Algorithms in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hasanen A. Hammad ◽  
Habib ur Rehman ◽  
Yaé Ulrich Gaba
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
Convergence Theorems ◽  
Numerical Examples ◽  
Convex Feasibility ◽  
Split Feasibility

The goal of this manuscript is to establish strong convergence theorems for inertial shrinking projection and CQ algorithms to solve a split convex feasibility problem in real Hilbert spaces. Finally, numerical examples were obtained to discuss the performance and effectiveness of our algorithms and compare the proposed algorithms with the previous shrinking projection, hybrid projection, and inertial forward-backward methods.

scholarly journals WEAK AND STRONG CONVERGENCE THEOREMS OF ALGORITHMIC SCHEMES FOR THE MULTIPLE-SETS SPLIT FEASIBILITY PROBLEM

2021 ◽  
Vol 226 (15) ◽  
pp. 28-35
Author(s):  
Nguyễn Bường ◽  
Nguyễn Dương Nguyễn
Keyword(s):  
Strong Convergence ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Split Feasibility

Trong bài báo này, để giải bài toán chấp nhận tách đa tập (MSSFP) trong không gian Hilbert, chúng tôi trình bày một cách tiếp cận tổng quát để xây dựng các phương pháp lặp. Chúng tôi đề xuất một lược đồ thuật toán xâu trung bình với sự hội tụ yếu và một lược đồ thuật toán xâu trung bình với sự hội tụ mạnh. Lược đồ thuật toán xâu trung bình với sự hội tụ mạnh được xây dựng dựa trên phương pháp lặp tổng quát cho ánh xạ không giãn, trong đó cỡ bước được tính toán trực tiếp trong mỗi bước lặp mà không cần sử dụng chuẩn của toán tử. Những lược đồ thuật toán này không chỉ bao hàm những cải tiến của phương pháp lặp vòng và lặp đồng thời đã biết như những trường hợp riêng mà còn bao hàm cả những phương pháp lặp mới

scholarly journals Strong Convergence Theorems for Generalized Split Feasibility Problems in Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 892
Author(s):  
Xuejiao Zi ◽  
Zhaoli Ma ◽  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Split Feasibility Problem ◽  
Fixed Point Problems ◽  
Feasibility Problem ◽  
Convergence Theorems ◽  
Split Common Fixed Point ◽  
Split Feasibility

In this paper, we establish new strong convergence theorems of proposed algorithms under suitable new conditions for the generalized split feasibility problem in Banach spaces. As applications, new strong convergence theorems for equilibrium problems, fixed point problems and split common fixed point problems are also studied. Our new results are distinct from recent results on the topic in the literature.

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