Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces

In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One of them is the set of zero points of the sum of two monotone operators and the other is the set of fixed points of mappings. By using the mo...

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Published in:Journal of inequalities and applications Vol. 2018; no. 1; pp. 289 - 15
Main Authors: Zhu, Jinhua, Tang, Jinfang, Chang, Shih-sen
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 2018
Springer Nature B.V
SpringerOpen
Subjects:
Algorithms
Analysis
Applications of Mathematics
Convergence
Feasibility
Fixed point problems
Fixed points (mathematics)
Hilbert space
Inverse strongly monotone operator
Iterative algorithms
Mathematics
Mathematics and Statistics
Maximal monotone operators
Split feasibility
Strong convergence theorems
Theorems
47H10
Maximal monotone operators
Strong convergence theorems
Inverse strongly monotone operator
Split feasibility
Fixed point problems
47H05
26A18
47H04
ISSN:1029-242X, 1025-5834, 1029-242X
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Abstract In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One of them is the set of zero points of the sum of two monotone operators and the other is the set of fixed points of mappings. By using the modified forward–backward splitting method, we propose a viscosity iterative algorithm. Under suitable conditions, some strong convergence theorems of the sequence generated by the algorithm to a common solution of the problem are proved. At the end of the paper, some applications and the constructed algorithm are also discussed.
AbstractList In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One of them is the set of zero points of the sum of two monotone operators and the other is the set of fixed points of mappings. By using the modified forward-backward splitting method, we propose a viscosity iterative algorithm. Under suitable conditions, some strong convergence theorems of the sequence generated by the algorithm to a common solution of the problem are proved. At the end of the paper, some applications and the constructed algorithm are also discussed.In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One of them is the set of zero points of the sum of two monotone operators and the other is the set of fixed points of mappings. By using the modified forward-backward splitting method, we propose a viscosity iterative algorithm. Under suitable conditions, some strong convergence theorems of the sequence generated by the algorithm to a common solution of the problem are proved. At the end of the paper, some applications and the constructed algorithm are also discussed.
In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One of them is the set of zero points of the sum of two monotone operators and the other is the set of fixed points of mappings. By using the modified forward–backward splitting method, we propose a viscosity iterative algorithm. Under suitable conditions, some strong convergence theorems of the sequence generated by the algorithm to a common solution of the problem are proved. At the end of the paper, some applications and the constructed algorithm are also discussed.
Abstract In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One of them is the set of zero points of the sum of two monotone operators and the other is the set of fixed points of mappings. By using the modified forward–backward splitting method, we propose a viscosity iterative algorithm. Under suitable conditions, some strong convergence theorems of the sequence generated by the algorithm to a common solution of the problem are proved. At the end of the paper, some applications and the constructed algorithm are also discussed.
ArticleNumber 289
Author Zhu, Jinhua
Chang, Shih-sen
Tang, Jinfang
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  givenname: Jinhua
  surname: Zhu
  fullname: Zhu, Jinhua
  organization: Department of Mathematics, Yibin University
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  givenname: Jinfang
  surname: Tang
  fullname: Tang, Jinfang
  organization: Department of Mathematics, Yibin University
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  givenname: Shih-sen
  surname: Chang
  fullname: Chang, Shih-sen
  email: changss2013@163.com
  organization: Center for General Education, China Medical University
BackLink https://www.ncbi.nlm.nih.gov/pubmed/30839719$$D View this record in MEDLINE/PubMed
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Cites_doi 10.1007/s10957-010-9713-2
10.1016/j.na.2011.03.041
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Issue 1
Keywords 47H10
Maximal monotone operators
Strong convergence theorems
Inverse strongly monotone operator
Split feasibility
Fixed point problems
47H05
26A18
47H04
Language English
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Snippet In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One...
Abstract In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert...
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StartPage 289
SubjectTerms Algorithms
Analysis
Applications of Mathematics
Convergence
Feasibility
Fixed point problems
Fixed points (mathematics)
Hilbert space
Inverse strongly monotone operator
Iterative algorithms
Mathematics
Mathematics and Statistics
Maximal monotone operators
Split feasibility
Strong convergence theorems
Theorems
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Title Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces
URI https://link.springer.com/article/10.1186/s13660-018-1881-x
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Volume 2018
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