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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Veröffentlicht in:	Advances in difference equations Jg. 2021; H. 1; S. 1 - 23
Hauptverfasser:	Arfat, Yasir, Kumam, Poom, Khan, Muhammad Aqeel Ahmad, Ngiamsunthorn, Parinya Sa, Kaewkhao, Attapol
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Cham Springer International Publishing 24.02.2021 Springer Nature B.V SpringerOpen
Schlagworte:	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
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Abstract	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.
AbstractList	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. Abstract 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.
ArticleNumber	124
Author	Ngiamsunthorn, Parinya Sa Kumam, Poom Arfat, Yasir Khan, Muhammad Aqeel Ahmad Kaewkhao, Attapol
Author_xml	– sequence: 1 givenname: Yasir surname: Arfat fullname: Arfat, Yasir organization: KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) – sequence: 2 givenname: Poom surname: Kumam fullname: Kumam, Poom email: poom.kumam@mail.kmutt.ac.th organization: KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), Department of Medical Research, China Medical University Hospital, China Medical University – sequence: 3 givenname: Muhammad Aqeel Ahmad surname: Khan fullname: Khan, Muhammad Aqeel Ahmad organization: Department of Mathematics, COMSATS University Islamabad – sequence: 4 givenname: Parinya Sa surname: Ngiamsunthorn fullname: Ngiamsunthorn, Parinya Sa organization: Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) – sequence: 5 givenname: Attapol surname: Kaewkhao fullname: Kaewkhao, Attapol organization: Research Center in Mathematics and Applied Mathematics, Faculty of Science, Chiang Mai University
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Cites_doi	10.1007/978-1-4613-0239-1 10.1007/BF02142692 10.1007/s11228-014-0285-4 10.1007/978-1-4419-9467-7 10.1088/0266-5611/21/6/017 10.1137/050626090 10.1137/0716071 10.1016/j.na.2005.08.018 10.1137/0329006 10.1007/s11075-011-9490-5 10.1016/j.chaos.2020.109685 10.1090/S0002-9947-1970-0282272-5 10.1002/mma.6155 10.1016/j.aej.2019.12.007 10.1137/S1052623403427859 10.1016/0041-5553(64)90137-5 10.1186/s13662-020-02956-8 10.1090/S0002-9947-1956-0084194-4 10.1140/epjp/i2018-12119-6 10.1016/j.chaos.2019.109477 10.1016/0022-247X(77)90076-2 10.1155/2012/109236 10.1186/s13662-020-02915-3 10.1016/S1076-5670(08)70157-5 10.1007/s10957-011-9814-6 10.1088/0031-9155/51/10/001 10.1137/0314056 10.1016/j.jmaa.2005.03.002
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Snippet	In this paper, we develop an iterative algorithm whose architecture comprises a modified version of the forward–backward splitting algorithm and the hybrid... Abstract In this paper, we develop an iterative algorithm whose architecture comprises a modified version of the forward–backward splitting algorithm and the...
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SubjectTerms	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
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Title	An inertially constructed forward–backward splitting algorithm in Hilbert spaces
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