Weak and Strong Convergence of Two Algorithms for the Split Fixed Point Problem

被引：15

作者：

Wang, Fenghui ^{[1
]}

Xu, Hong-Kun ^{[2
]}

机构：

[1] Luoyang Normal Univ, Dept Math, Luoyang 471022, Peoples R China

[2] Hangzhou Dianzi Univ, Sch Sci, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

来源：

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2018年 / 11卷 / 04期

关键词：

Split feasibility; fixed point; Fejer-monotonicity; nonexpansive mapping; projection; iterative algorithm; ITERATIVE ALGORITHMS; PROJECTION;

D O I：

10.4208/nmtma.2018.s05

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two iterative algorithms are proposed for the split fixed point problem. The first algorithm is shown to be weakly convergent and the second one to be strongly convergent. One feature of these algorithms is that the stepsizes are chosen in such a way that no priori knowledge of the operator norms is required. A new idea is introduced in order to prove strong convergence of the second algorithm.

引用

页码：770 / 781

页数：12

共 26 条

[11] FIXED POINTS OF NONEXPANDING MAPS [J].

HALPERN, B .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 73 (06) :957-&

[12] On split common fixed point problems [J].

Kraikaew, Rapeepan ;

Saejung, Satit .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 415 (02) :513-524

[13] Solving the split feasibility problem without prior knowledge of matrix norms [J].

Lopez, Genaro ;

Martin-Marquez, Victoria ;

Wang, Fenghui ;

Xu, Hong-Kun .

INVERSE PROBLEMS, 2012, 28 (08)

[14]

López G, 2010, CONTEMP MATH, V513, P211

[15] A note on the split common fixed-point problem for quasi-nonexpansive operators [J].

Moudafi, A. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (12) :4083-4087

[16] The split common fixed-point problem for demicontractive mappings [J].

Moudafi, A. .

INVERSE PROBLEMS, 2010, 26 (05)

[17] WEAK CONVERGENCE OF SEQUENCE OF SUCCESSIVE APPROXIMATIONS FOR NONEXPANSIVE MAPPINGS [J].

OPIAL, Z .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 73 (04) :591-&

[18] APPROXIMATING FIXED-POINTS OF NONEXPANSIVE-MAPPINGS BY THE ISHIKAWA ITERATION PROCESS [J].

TAN, KK ;

XU, HK .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 178 (02) :301-308

[19] On the convergence of CQ algorithm with variable steps for the split equality problem [J].

Wang, Fenghui .

NUMERICAL ALGORITHMS, 2017, 74 (03) :927-935

[20] A new iterative method for the split common fixed point problem in Hilbert spaces [J].

Wang, Fenghui .

OPTIMIZATION, 2017, 66 (03) :407-415

← 1 2 3 →