Completely generalized multivalued nonlinear quasi-variational inclusions

Zeqing Liu, Lokenath Debnath, Shin Min Kang and Jeong Sheok Ume

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 30, 1-12

Abstract:

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.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:479161

DOI: 10.1155/S0161171202108283

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