Completely generalized multivalued nonlinear quasi-variational inclusions
We introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-varia...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202108283 |
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| author | Zeqing Liu Lokenath Debnath Shin Min Kang Jeong Sheok Ume |
| author_facet | Zeqing Liu Lokenath Debnath Shin Min Kang Jeong Sheok Ume |
| author_sort | Zeqing Liu |
| collection | DOAJ |
| description | We introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou-Yao, Kazmi, Noor, Noor-Al-Said, Noor-Noor, Noor-Noor-Rassias, Shim-Kang-Huang-Cho, Siddiqi-Ansari, Verma, Yao, and Zhang. |
| format | Article |
| id | doaj-art-95df40e5995d468d930926c8a4e3b708 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-95df40e5995d468d930926c8a4e3b7082025-08-20T03:20:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01301059360410.1155/S0161171202108283Completely generalized multivalued nonlinear quasi-variational inclusionsZeqing Liu0Lokenath Debnath1Shin Min Kang2Jeong Sheok Ume3Department of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, ChinaDepartment of Mathematics, University of Texas, Pan American, Edinburg, Texas 78539, USADepartment of Mathematics, Gyeongsang National University, Chinju 660-701, KoreaDepartment of Applied Mathematics, Changwon National University, Changwon 641-773, KoreaWe introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou-Yao, Kazmi, Noor, Noor-Al-Said, Noor-Noor, Noor-Noor-Rassias, Shim-Kang-Huang-Cho, Siddiqi-Ansari, Verma, Yao, and Zhang.http://dx.doi.org/10.1155/S0161171202108283 |
| spellingShingle | Zeqing Liu Lokenath Debnath Shin Min Kang Jeong Sheok Ume Completely generalized multivalued nonlinear quasi-variational inclusions International Journal of Mathematics and Mathematical Sciences |
| title | Completely generalized multivalued nonlinear quasi-variational inclusions |
| title_full | Completely generalized multivalued nonlinear quasi-variational inclusions |
| title_fullStr | Completely generalized multivalued nonlinear quasi-variational inclusions |
| title_full_unstemmed | Completely generalized multivalued nonlinear quasi-variational inclusions |
| title_short | Completely generalized multivalued nonlinear quasi-variational inclusions |
| title_sort | completely generalized multivalued nonlinear quasi variational inclusions |
| url | http://dx.doi.org/10.1155/S0161171202108283 |
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