An inertially constructed forward–backward splitting algorithm in Hilbert spaces

In this paper, we develop an iterative algorithm whose architecture comprises a modified version of the forward–backward splitting algorithm and the hybrid shrinking projection algorithm. We provide theoretical results concerning weak and strong convergence of the proposed algorithm towards a common...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2021; no. 1; pp. 1 - 23
Main Authors: Arfat, Yasir, Kumam, Poom, Khan, Muhammad Aqeel Ahmad, Ngiamsunthorn, Parinya Sa, Kaewkhao, Attapol
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 24.02.2021
Springer Nature B.V
SpringerOpen
Subjects:
Algorithms
Analysis
Demicontractive operator
Difference and Functional Equations
Fixed point problem
Fixed points (mathematics)
Forward–backward splitting algorithm
Functional Analysis
Hilbert space
Hilbert spaces
Iterative algorithms
Iterative methods
Mathematics
Mathematics and Statistics
Monotone inclusion problem
Ordinary Differential Equations
Partial Differential Equations
Split equilibrium problem
Splitting
Demicontractive operator
Fixed point problem
47H10
65K05
90C25
Split equilibrium problem
Monotone inclusion problem
Hilbert spaces
Forward–backward splitting algorithm
47H05
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary:In this paper, we develop an iterative algorithm whose architecture comprises a modified version of the forward–backward splitting algorithm and the hybrid shrinking projection algorithm. We provide theoretical results concerning weak and strong convergence of the proposed algorithm towards a common solution of the fixed point problem associated to a finite family of demicontractive operators, the split equilibrium problem and the monotone inclusion problem in Hilbert spaces. Moreover, we compute a numerical experiment to show the efficiency of the proposed algorithm. As a consequence, our results improve various existing results in the current literature.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03277-0