Existence result and error bounds for a new class of inverse mixed quasi-variational inequalities
Abstract In this paper, a new class of inverse mixed quasi-variational inequalities (IMQVI) is introduced and studied in Hilbert spaces. This type of inequalities includes many quasi-variational inequalities and inverse variational inequalities as its special cases. We first prove some properties of...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-02-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-0968-5 |
| _version_ | 1828475656833335296 |
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| author | Xi Li Yun-zhi Zou |
| author_facet | Xi Li Yun-zhi Zou |
| author_sort | Xi Li |
| collection | DOAJ |
| description | Abstract In this paper, a new class of inverse mixed quasi-variational inequalities (IMQVI) is introduced and studied in Hilbert spaces. This type of inequalities includes many quasi-variational inequalities and inverse variational inequalities as its special cases. We first prove some properties of generalized f-projection operators in Hilbert spaces. Then we use these properties to obtain the existence and uniqueness result. Moreover, error bounds for IMQVI in terms of the residual function are also established. The results presented in this paper are new and improve some results in the recent literature. |
| first_indexed | 2024-12-11T06:17:22Z |
| format | Article |
| id | doaj.art-31148b082cdf4698bed2053f1f98d188 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-11T06:17:22Z |
| publishDate | 2016-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-31148b082cdf4698bed2053f1f98d1882022-12-22T01:17:56ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-02-012016111310.1186/s13660-016-0968-5Existence result and error bounds for a new class of inverse mixed quasi-variational inequalitiesXi Li0Yun-zhi Zou1School of Science, Xihua UniversityDepartment of Mathematics, Sichuan UniversityAbstract In this paper, a new class of inverse mixed quasi-variational inequalities (IMQVI) is introduced and studied in Hilbert spaces. This type of inequalities includes many quasi-variational inequalities and inverse variational inequalities as its special cases. We first prove some properties of generalized f-projection operators in Hilbert spaces. Then we use these properties to obtain the existence and uniqueness result. Moreover, error bounds for IMQVI in terms of the residual function are also established. The results presented in this paper are new and improve some results in the recent literature.http://link.springer.com/article/10.1186/s13660-016-0968-5mixed variational inequalityinverse mixed quasi-variational inequalitygeneralized f-projection operatorerror boundresidual function |
| spellingShingle | Xi Li Yun-zhi Zou Existence result and error bounds for a new class of inverse mixed quasi-variational inequalities Journal of Inequalities and Applications mixed variational inequality inverse mixed quasi-variational inequality generalized f-projection operator error bound residual function |
| title | Existence result and error bounds for a new class of inverse mixed quasi-variational inequalities |
| title_full | Existence result and error bounds for a new class of inverse mixed quasi-variational inequalities |
| title_fullStr | Existence result and error bounds for a new class of inverse mixed quasi-variational inequalities |
| title_full_unstemmed | Existence result and error bounds for a new class of inverse mixed quasi-variational inequalities |
| title_short | Existence result and error bounds for a new class of inverse mixed quasi-variational inequalities |
| title_sort | existence result and error bounds for a new class of inverse mixed quasi variational inequalities |
| topic | mixed variational inequality inverse mixed quasi-variational inequality generalized f-projection operator error bound residual function |
| url | http://link.springer.com/article/10.1186/s13660-016-0968-5 |
| work_keys_str_mv | AT xili existenceresultanderrorboundsforanewclassofinversemixedquasivariationalinequalities AT yunzhizou existenceresultanderrorboundsforanewclassofinversemixedquasivariationalinequalities |