An explicit parallel algorithm for solving variational inclusion problem and fixed point problem in Banach spaces

被引：19

作者：

Cholamjiak, Prasit ^{[1
]}

Suantai, Suthep ^{[2
]}

Sunthrayuth, Pongsakorn ^{[3
]}

机构：

[1] Univ Phayao, Sch Sci, Phayao 56000, Thailand

[2] Chiang Mai Univ, Fac Sci, Res Ctr Math & Appl Math, Dept Math, Chiang Mai 50200, Thailand

[3] Rajamangala Univ Technol Thanyaburi RMUTT, Fac Sci & Technol, Dept Math & Comp Sci, Pathum Thani 12110, Thailand

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2020年 / 14卷 / 01期

关键词：

Variational inclusion; Banach space; Strong convergence; Accretive operator; ITERATIVE ALGORITHMS; MONOTONICITY; CONVERGENCE;

D O I：

10.1007/s43037-019-00030-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we introduce an explicit parallel algorithm for finding a common element of zeros of the sum of two accretive operators and the set of fixed point of a nonexpansive mapping in the framework of Banach spaces. We prove its strong convergence under some mild conditions. Finally, we provide some applications to the main result. The results presented in this paper extend and improve the corresponding results in the literature.

引用

页码：20 / 40

页数：21

共 50 条

[21] Halpern-type iterative process for solving split common fixed point and monotone variational inclusion problem between Banach spaces
Taiwo, A.
Alakoya, T. O.
Mewomo, O. T.
NUMERICAL ALGORITHMS, 2021, 86 (04) : 1359 - 1389
[22] Iteration process for solving a fixed point problem of nonexpansive mappings in Banach spaces
Khoonyang S.
Inta M.
Cholamjiak P.
Afrika Matematika, 2018, 29 (5-6) : 783 - 792
[23] PARALLEL ITERATIVE METHODS FOR SOLVING THE COMMON NULL POINT PROBLEM IN BANACH SPACES
Truong Minh Tuyen
Nguyen Minh Trang
ADVANCES IN OPERATOR THEORY, 2018, 3 (03) : 606 - 619
[24] A COMPOSITE SPLITTING ALGORITHM FOR SOLVING FIXED POINT AND VARIATIONAL INCLUSION PROBLEMS IN HILBERT SPACES
Zhao, Xiaopeng
Zhao, Yufei
UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2022, 84 (03): : 21 - 30
[25] Strong convergence theorems for the split equality variational inclusion problem and fixed point problem in Hilbert spaces
Haili Guo
Huimin He
Rudong Chen
Fixed Point Theory and Applications, 2015
[26] AN INERTIAL BREGMAN HYBRID ALGORITHM FOR APPROXIMATING SOLUTIONS OF FIXED POINT AND VARIATIONAL INEQUALITY PROBLEM IN REAL BANACH SPACES
Ali, Bashir
Hamza, A. M.
Harbau, M. H.
MATEMATICKI VESNIK, 2022, 74 (03): : 174 - 188
[27] Strong convergence theorems for the split equality variational inclusion problem and fixed point problem in Hilbert spaces
Guo, Haili
He, Huimin
Chen, Rudong
FIXED POINT THEORY AND APPLICATIONS, 2015, : 1 - 18
[28] Split Variational Inclusion Problem and Fixed Point Problem for a Class of Multivalued Mappings in CAT(0) Spaces
Abbas, Mujahid
Ibrahim, Yusuf
Khan, Abdul Rahim
De la Sen, Manuel
MATHEMATICS, 2019, 7 (08)
[29] Minimum-norm solution of variational inequality and fixed point problem in banach spaces
Zegeye, Habtu
Shahzad, Naseer
Yao, Yonghong
OPTIMIZATION, 2015, 64 (02) : 453 - 471
[30] The generalized viscosity explicit rules for solving variational inclusion problems in Banach spaces
Cholamjiak, Prasit
Pholasa, Nattawut
Suantai, Suthep
Sunthrayuth, Pongsakorn
OPTIMIZATION, 2021, 70 (12) : 2607 - 2633

← 1 2 3 4 5 →