Asymptotic Behavior of a Discrete Nonlinear Oscillator with Damping Dynamical System
<p/> <p>We propose a new discrete version of nonlinear oscillator with damping dynamical system governed by a general maximal monotone operator. We show the weak convergence of solutions and their weighted averages to a zero of a maximal monotone operator <inline-formula><graphi...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2011/867136 |
| _version_ | 1811294375437664256 |
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| author | Khatibzadeh Hadi |
| author_facet | Khatibzadeh Hadi |
| author_sort | Khatibzadeh Hadi |
| collection | DOAJ |
| description | <p/> <p>We propose a new discrete version of nonlinear oscillator with damping dynamical system governed by a general maximal monotone operator. We show the weak convergence of solutions and their weighted averages to a zero of a maximal monotone operator <inline-formula><graphic file="1687-1847-2011-867136-i1.gif"/></inline-formula>. We also prove some strong convergence theorems with additional assumptions on <inline-formula><graphic file="1687-1847-2011-867136-i2.gif"/></inline-formula>. This iterative scheme gives also an extension of the proximal point algorithm for the approximation of a zero of a maximal monotone operator. These results extend previous results by Brézis and Lions (1978), Lions (1978) as well as Djafari Rouhani and H. Khatibzadeh (2008).</p> |
| first_indexed | 2024-04-13T05:16:37Z |
| format | Article |
| id | doaj.art-64dcffa03fb843c1bd7ce903c577ab28 |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-04-13T05:16:37Z |
| publishDate | 2011-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-64dcffa03fb843c1bd7ce903c577ab282022-12-22T03:00:53ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472011-01-0120111867136Asymptotic Behavior of a Discrete Nonlinear Oscillator with Damping Dynamical SystemKhatibzadeh Hadi<p/> <p>We propose a new discrete version of nonlinear oscillator with damping dynamical system governed by a general maximal monotone operator. We show the weak convergence of solutions and their weighted averages to a zero of a maximal monotone operator <inline-formula><graphic file="1687-1847-2011-867136-i1.gif"/></inline-formula>. We also prove some strong convergence theorems with additional assumptions on <inline-formula><graphic file="1687-1847-2011-867136-i2.gif"/></inline-formula>. This iterative scheme gives also an extension of the proximal point algorithm for the approximation of a zero of a maximal monotone operator. These results extend previous results by Brézis and Lions (1978), Lions (1978) as well as Djafari Rouhani and H. Khatibzadeh (2008).</p>http://www.advancesindifferenceequations.com/content/2011/867136 |
| spellingShingle | Khatibzadeh Hadi Asymptotic Behavior of a Discrete Nonlinear Oscillator with Damping Dynamical System Advances in Difference Equations |
| title | Asymptotic Behavior of a Discrete Nonlinear Oscillator with Damping Dynamical System |
| title_full | Asymptotic Behavior of a Discrete Nonlinear Oscillator with Damping Dynamical System |
| title_fullStr | Asymptotic Behavior of a Discrete Nonlinear Oscillator with Damping Dynamical System |
| title_full_unstemmed | Asymptotic Behavior of a Discrete Nonlinear Oscillator with Damping Dynamical System |
| title_short | Asymptotic Behavior of a Discrete Nonlinear Oscillator with Damping Dynamical System |
| title_sort | asymptotic behavior of a discrete nonlinear oscillator with damping dynamical system |
| url | http://www.advancesindifferenceequations.com/content/2011/867136 |
| work_keys_str_mv | AT khatibzadehhadi asymptoticbehaviorofadiscretenonlinearoscillatorwithdampingdynamicalsystem |