Weak- and strong-convergence theorems of solutions to split feasibility problem for nonspreading type mapping in Hilbert spaces

被引：41

作者：

Chang, Shih-sen ^{[1
]}

Kim, Jong Kyu ^{[2
]}

Cho, Yeol Je ^{[3
,4
]}

Sim, Jae Yull ^{[5
]}

机构：

[1] Yunnan Univ Finance & Econ, Coll Stat & Math, Kunming 650221, Yunnan, Peoples R China

[2] Kyungnam Univ, Dept Math Educ, Chang Won 631701, Gyeongnam, South Korea

[3] Gyeongsang Natl Univ, Dept Math Educ, Chinju 660701, South Korea

[4] Gyeongsang Natl Univ, RINS, Chinju 660701, South Korea

[5] Kyungnam Univ, Dept Math, Chang Won 631701, Gyeongnam, South Korea

来源：

FIXED POINT THEORY AND APPLICATIONS | 2014年

基金：

新加坡国家研究基金会;

关键词：

split feasibility problem; convex feasibility problem; k-strictly pseudo-nonspreading mapping; demicloseness; Opial's condition; SETS; ALGORITHM;

D O I：

10.1186/1687-1812-2014-11

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this article is to study the weak- and strong-convergence theorems of solutions to split a feasibility problem for a family of nonspreading-type mapping in Hilbert spaces. The main result presented in this paper improves and extends some recent results of Censor et al., Byrne, Yang, Moudafi, Xu, Censor and Segal, Masad and Reich, and others. As an application, we solve the hierarchical variational inequality problem by using the main theorem.

引用

页数：12

共 22 条

[1]

BAILLON JB, 1975, CR ACAD SCI A MATH, V280, P1511

[2] Iterative oblique projection onto convex sets and the split feasibility problem [J].

Byrne, C .

INVERSE PROBLEMS, 2002, 18 (02) :441-453

[3] 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

[4]

Censor Y., 1994, Numerical Algorithms, V8, P221, DOI DOI 10.1007/BF02142692

[5]

Censor Y, 2009, J CONVEX ANAL, V16, P587

[6] 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

[7] Perturbed projections and subgradient projections for the multiple-sets split feasibility problem [J].

Censor, Yair ;

Motova, Avi ;

Segal, Alexander .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 327 (02) :1244-1256

[8] Multiple-Set Split Feasibility Problems for Asymptotically Strict Pseudocontractions [J].

Chang, Shih-Sen ;

Cho, Yeol Je ;

Kim, J. K. ;

Zhang, W. B. ;

Yang, L. .

ABSTRACT AND APPLIED ANALYSIS, 2012,

[9] Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces [J].

Chang, Shih-sen ;

Kim, Jong Kyu ;

Wang, Xiong Rui .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2010,

[10] Split feasibility and fixed-point problems for asymptotically quasi-nonexpansive mappings [J].

Deepho, Jitsupa ;

Kumam, Poom .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,

← 1 2 3 →