New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications
Some new inertial forward-backward projection iterative algorithms are designed in a real Hilbert space. Under mild assumptions, some strong convergence theorems for common zero points of the sum of two kinds of infinitely many accretive mappings are proved. New projection sets are constructed which...
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| Format: | Article |
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MDPI AG
2019-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/5/466 |
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| author | Li Wei Yingzi Shang Ravi P. Agarwal |
| author_facet | Li Wei Yingzi Shang Ravi P. Agarwal |
| author_sort | Li Wei |
| collection | DOAJ |
| description | Some new inertial forward-backward projection iterative algorithms are designed in a real Hilbert space. Under mild assumptions, some strong convergence theorems for common zero points of the sum of two kinds of infinitely many accretive mappings are proved. New projection sets are constructed which provide multiple choices of the iterative sequences. Some already existing iterative algorithms are demonstrated to be special cases of ours. Some inequalities of metric projection and real number sequences are widely used in the proof of the main results. The iterative algorithms have also been modified and extended from pure discussion on the sum of accretive mappings or pure study on variational inequalities to that for both, which complements the previous work. Moreover, the applications of the abstract results on nonlinear capillarity systems are exemplified. |
| first_indexed | 2024-12-20T14:35:00Z |
| format | Article |
| id | doaj.art-5ff98a583c2c4409bd2372bbf5829368 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-20T14:35:00Z |
| publishDate | 2019-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5ff98a583c2c4409bd2372bbf58293682022-12-21T19:37:29ZengMDPI AGMathematics2227-73902019-05-017546610.3390/math7050466math7050466New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and ApplicationsLi Wei0Yingzi Shang1Ravi P. Agarwal2School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaSchool of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaDepartment of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USASome new inertial forward-backward projection iterative algorithms are designed in a real Hilbert space. Under mild assumptions, some strong convergence theorems for common zero points of the sum of two kinds of infinitely many accretive mappings are proved. New projection sets are constructed which provide multiple choices of the iterative sequences. Some already existing iterative algorithms are demonstrated to be special cases of ours. Some inequalities of metric projection and real number sequences are widely used in the proof of the main results. The iterative algorithms have also been modified and extended from pure discussion on the sum of accretive mappings or pure study on variational inequalities to that for both, which complements the previous work. Moreover, the applications of the abstract results on nonlinear capillarity systems are exemplified.https://www.mdpi.com/2227-7390/7/5/466m-accretive mappingstrongly positive mapping<i>μ</i>-inversely strongly accretive mapping<i>τ</i>-Lipschitz continuous mappingvariational inequalitiescapillarity systems |
| spellingShingle | Li Wei Yingzi Shang Ravi P. Agarwal New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications Mathematics m-accretive mapping strongly positive mapping <i>μ</i>-inversely strongly accretive mapping <i>τ</i>-Lipschitz continuous mapping variational inequalities capillarity systems |
| title | New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications |
| title_full | New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications |
| title_fullStr | New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications |
| title_full_unstemmed | New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications |
| title_short | New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications |
| title_sort | new inertial forward backward mid point methods for sum of infinitely many accretive mappings variational inequalities and applications |
| topic | m-accretive mapping strongly positive mapping <i>μ</i>-inversely strongly accretive mapping <i>τ</i>-Lipschitz continuous mapping variational inequalities capillarity systems |
| url | https://www.mdpi.com/2227-7390/7/5/466 |
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