Generalized Nonlinear Fuzzy Quasi-Variational-Like Inclusions Involving Maximal η-Monotone Mappings

In this paper, we introduce and study a new class of generalized nonlinear fuzzy quasi-variational-like inclusions involving maximal η-monotone mappings. We construct some new iterative algorithms with errors for solving these generalized fuzzy variational inclusions by using the resolvent operator technique for maximal η-monotone mappings and prove the convergence of iterative sequences generated by the algorithms. We also discuss the convergence and stability of perturbed iterative algorithm for solving a class of generalized nonlinear quasi-variational-like inclusions involving maximal η-monotone mappings.First, we show the real background of the problems that we study, which comes from some optimization problems in economics, engineering, the social and physical sciences, and other applied science, and we introduce the main works that have been studied by many authors, so as to show that our works worthy of attention. Second, we introduce some basic conceptions, especially the definition of maximal η-rnonotone mapping introduced by Huang and Fang, and in the three section, we introduce the studied problem and its some specail cases, and give some correlative important proposition and lemmas. Our main results are in the last two sections. Section 4 is devoted to give some new iterative algorithms with errors. With some noncompact constraint qualifications, we prove the existence of solution for the generalized nonlinear fuzzy quasi-variational-like inclusions involving maximal η-monotone mappings and the convergence of iterative sequences generated by the iterative algorithms. In the last, we discuss the convergence and stability of perturbed iterative algorithm for solving aclass of generalized nonlinear quasi-variational-like inclusions involving maximal η-monotone mappings.Our results improve and generalize many known corresponding results.