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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Vydáno v:Journal of inequalities and applications Ročník 2018; číslo 1; s. 289 - 15
Hlavní autoři: Zhu, Jinhua, Tang, Jinfang, Chang, Shih-sen
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 2018
Springer Nature B.V
SpringerOpen
Témata:
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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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-018-1881-x