Iterative Algorithms for a System of Variational Inclusions Involving Set-Valued Quasi-Contractive Mappings in Banach Spaces

被引:4
作者
Qiu, Yangqing [1 ]
Liu, Xiaomei [1 ]
机构
[1] Shanghai Polytech Univ, Dept Math, Shanghai 201209, Peoples R China
关键词
Convergence; fixed point; iterative algorithm; quasi-contractive mapping; system of variational inclusions; CONVERGENCE;
D O I
10.1080/01630563.2021.1933519
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, a new system of variational inclusions involving set-valued quasi-contractive, lower semi-continuous mappings with nonempty closed and convex values is introduced and studied in real Banach spaces. First, both the existence of fixed points of the set-valued quasi-contractive mappings and the solution of the system of variational inclusions are proved. Then, using the existence result, a new iterative algorithm is constructed. And then the strong convergence of the iterative sequences is proved, and the proof is novel. Finally, a numerical example is given to demonstrate the algorithm. Our results improve and extend some known results.
引用
收藏
页码:865 / 882
页数:18
相关论文
共 16 条
[1]   Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces [J].
Agarwal, RP ;
Cho, YJ ;
Li, J ;
Huang, NJ .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 272 (02) :435-447
[2]   A class of quasicontractive semigroups acting on Hardy and weighted Hardy spaces [J].
Chalendar, I. ;
Partington, J. R. .
SEMIGROUP FORUM, 2017, 95 (02) :281-292
[3]   Set-valued variational inclusions in Banach spaces [J].
Chang, SS .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 248 (02) :438-454
[4]   Convergence of over-relaxed contraction-proximal point algorithm in Hilbert spaces [J].
Cui, Huanhuan ;
Ceng, Luchuan .
OPTIMIZATION, 2017, 66 (05) :793-809
[5]   A strong convergence result involving an inertial forward-backward algorithm for monotone inclusions [J].
Dong, Qiaoli ;
Jiang, Dan ;
Cholamjiak, Prasit ;
Shehu, Yekini .
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2017, 19 (04) :3097-3118
[6]  
Frankowska H., 2009, SET-VALUED ANAL
[7]   An alternating iteration algorithm for solving the split equality fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings [J].
Li, Meixia ;
Zhou, Xueling ;
Che, Haitao .
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2019, 2019 (01)
[8]   CONTINUOUS SELECTIONS .1. [J].
MICHAEL, E .
ANNALS OF MATHEMATICS, 1956, 63 (02) :361-382
[9]   MULTI-VALUED CONTRACTION MAPPINGS [J].
NADLER, SB .
PACIFIC JOURNAL OF MATHEMATICS, 1969, 30 (02) :475-&
[10]   Generalized set-valued variational inclusions and resolvent equations [J].
Noor, MA .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 228 (01) :206-220