Quasi-variational Inequality And Variational Inclusions For Fuzzy Mapping

In this paper, we introduce and study a new class of quasi-variational inequalitiy for fuzzy mapping in Hilbert space. We prove the existence of a solution for this kind of quasi-variational inequality and construct the iterative algorithm for the quasi-variational inequality.We get the convergence of iterative sequences generated by the algorithm.We also introduce and study a new system generalized nonlinear variational inclusions for fuzzy mappings in Hilbert space. We establish the equivalence between the new system of variational inclusions for fuzzy mappings and fixed point problem of nonlinear set-valued mappings by employing the resolvent operator technique for maximal monotone mapping ,and then, by using Nadler's fixed point theorem, give an existence theorem of solution for the variational inclusions.The results presented in this paper improve and extend many known earlier results in this area.