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.
Highlights
In 1996, Adly [1] used the resolvent operator technique for maximal monotone mapping to study a general class of variational inclusions with singlevalued mappings
We first introduce a new class of completely generalized multivalued nonlinear quasi-variational inclusions for multivalued mappings
We establish four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz and generalized pseudocontractive multivalued mappings, and give some convergence results of iterative sequences generated by the algorithms
Summary
In 1996, Adly [1] used the resolvent operator technique for maximal monotone mapping to study a general class of variational inclusions with singlevalued mappings.
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