Weak and strong convergence theorems for the split common fixed point problem with demicontractive operators

被引：14
作者：
Fan, Qinwei [1 ,2 ]
Peng, Jigen [1 ]
He, Huimin [3 ]
机构：
[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou, Peoples R China
[2] Xian Polytech Univ, Sch Sci, Xian, Peoples R China
[3] Xidian Univ, Sch Math & Stat, Xian, Peoples R China
来源：
OPTIMIZATION | 2021年 / 70卷 / 5-6期
基金：
中国博士后科学基金;
关键词：
Split common fixed point problem; demicontractive mapping; weak convergence; strong convergence; CQ-ALGORITHM;
D O I：
10.1080/02331934.2021.1890074
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
A novel iterative algorithm is introduced for solving the split common fixed point problem with demicontractive operators. Weak and strong convergence of the algorithm is discussed. The step-sizes of the algorithm are chosen in such a way that the implementation of the algorithm does not depend on operator norms. The main results proven in this paper extend and improve some results of Yao et al. [Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem. Fixed Point Theor Appl. 2014;2014:183], Boikanyo [A strongly convergent algorithm for the split common fixed point problem. Appl Math Comput. 2015;265:844-853] and Cui and Wang [Iterative methods for the split common fixed point problem in Hilbert spaces. Fixed Point Theor Appl. 2014;2014:78].
引用
收藏
页码：1409 / 1423
页数：15
相关论文
共 35 条
[1]   A strongly convergent algorithm for the split common fixed point problem [J].
Boikanyo, Oganeditse A. .
APPLIED MATHEMATICS AND COMPUTATION, 2015, 265 :844-853
[2]   Iterative oblique projection onto convex sets and the split feasibility problem [J].
Byrne, C .
INVERSE PROBLEMS, 2002, 18 (02) :441-453
[3]   A unified treatment of some iterative algorithms in signal processing and image reconstruction [J].
Byrne, C .
INVERSE PROBLEMS, 2004, 20 (01) :103-120
[4]   Block-iterative methods for image reconstruction from projections [J].
Byrne, CL .
IEEE TRANSACTIONS ON IMAGE PROCESSING, 1996, 5 (05) :792-794
[5]   Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem [J].
Ceng, L. -C. ;
Ansari, Q. H. ;
Yao, J. -C. .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) :2116-2125
[6]   The multiple-sets split feasibility problem and its applications for inverse problems [J].
Censor, Y ;
Elfving, T ;
Kopf, N ;
Bortfeld, T .
INVERSE PROBLEMS, 2005, 21 (06) :2071-2084
[7]  
Censor Y., 1994, NUMER ALGORITHMS, V8, P221, DOI [DOI 10.1007/BF02142692, 10.1007/BF02142692]
[8]  
Censor Y, 2009, J CONVEX ANAL, V16, P587
[9]   A unified approach for inversion problems in intensity-modulated radiation therapy [J].
Censor, Yair ;
Bortfeld, Thomas ;
Martin, Benjamin ;
Trofimov, Alexei .
PHYSICS IN MEDICINE AND BIOLOGY, 2006, 51 (10) :2353-2365
[10]   Split equality fixed point problem for quasi-pseudo-contractive mappings with applications [J].
Chang, Shih-sen ;
Wang, Lin ;
Qin, Li-Juan .
FIXED POINT THEORY AND APPLICATIONS, 2015, :1-12
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