A Valuable Remark on Lipschitz in the First Variable Definition and System of Nonlinear Variational Inequalities
The goal of this paper is to present a critique on the incorrect use of the Lipschitz definition concerning the first variable and/or the second variable in the literature on the system of variational inequalities by many authors. The possible impact of this paper is rather important, it questions t...
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| Format: | Article |
| Language: | English |
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Croatian Operational Research Society
2022-01-01
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| Series: | Croatian Operational Research Review |
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| Online Access: | https://hrcak.srce.hr/file/406250 |
| _version_ | 1797206666162208768 |
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| author | Ayache Benhadid |
| author_facet | Ayache Benhadid |
| author_sort | Ayache Benhadid |
| collection | DOAJ |
| description | The goal of this paper is to present a critique on the incorrect use of the Lipschitz definition concerning the first variable and/or the second variable in the literature on the system of variational inequalities by many authors. The possible impact of this paper is rather important, it questions the results of different authors, particularly when taking into account that some of these papers are published in quite good mathematical journals. As a result, not only that the proofs are wrong, but also the credibility of the theorems themselves is compromised. In addition, this paper illustrate, using a counterexample, that there is an error in setting up first variable definition and the results obtained in listed references do not hold up in H × H. |
| first_indexed | 2024-04-24T09:10:38Z |
| format | Article |
| id | doaj.art-9a1fa5e4dd714be9a20e2a1b03936997 |
| institution | Directory Open Access Journal |
| issn | 1848-0225 1848-9931 |
| language | English |
| last_indexed | 2024-04-24T09:10:38Z |
| publishDate | 2022-01-01 |
| publisher | Croatian Operational Research Society |
| record_format | Article |
| series | Croatian Operational Research Review |
| spelling | doaj.art-9a1fa5e4dd714be9a20e2a1b039369972024-04-15T17:51:37ZengCroatian Operational Research SocietyCroatian Operational Research Review1848-02251848-99312022-01-0113113113510.17535/crorr.2022.0009A Valuable Remark on Lipschitz in the First Variable Definition and System of Nonlinear Variational InequalitiesAyache Benhadid0Department of Mathematics, Faculty of Mathematics and Computer ScienceThe goal of this paper is to present a critique on the incorrect use of the Lipschitz definition concerning the first variable and/or the second variable in the literature on the system of variational inequalities by many authors. The possible impact of this paper is rather important, it questions the results of different authors, particularly when taking into account that some of these papers are published in quite good mathematical journals. As a result, not only that the proofs are wrong, but also the credibility of the theorems themselves is compromised. In addition, this paper illustrate, using a counterexample, that there is an error in setting up first variable definition and the results obtained in listed references do not hold up in H × H.https://hrcak.srce.hr/file/406250Lipschitz continuous mappingsSystem of variational inequalities with different nonlinear mappings |
| spellingShingle | Ayache Benhadid A Valuable Remark on Lipschitz in the First Variable Definition and System of Nonlinear Variational Inequalities Croatian Operational Research Review Lipschitz continuous mappings System of variational inequalities with different nonlinear mappings |
| title | A Valuable Remark on Lipschitz in the First Variable Definition and System of Nonlinear Variational Inequalities |
| title_full | A Valuable Remark on Lipschitz in the First Variable Definition and System of Nonlinear Variational Inequalities |
| title_fullStr | A Valuable Remark on Lipschitz in the First Variable Definition and System of Nonlinear Variational Inequalities |
| title_full_unstemmed | A Valuable Remark on Lipschitz in the First Variable Definition and System of Nonlinear Variational Inequalities |
| title_short | A Valuable Remark on Lipschitz in the First Variable Definition and System of Nonlinear Variational Inequalities |
| title_sort | valuable remark on lipschitz in the first variable definition and system of nonlinear variational inequalities |
| topic | Lipschitz continuous mappings System of variational inequalities with different nonlinear mappings |
| url | https://hrcak.srce.hr/file/406250 |
| work_keys_str_mv | AT ayachebenhadid avaluableremarkonlipschitzinthefirstvariabledefinitionandsystemofnonlinearvariationalinequalities AT ayachebenhadid valuableremarkonlipschitzinthefirstvariabledefinitionandsystemofnonlinearvariationalinequalities |