Fuzzy nonlinear set-valued variational inclusions

The purpose of this paper is to study a new class of fuzzy nonlinear set-valued variational inclusions in real Banach spaces. By using the fuzzy resolvent operator techniques for mm-accretive mappings, we establish the equivalence between fuzzy nonlinear set-valued variational inclusions and fuzzy resolvent operator equation problem. Applying this equivalence and Nadler’s theorem, we suggest some iterative algorithms for solving fuzzy nonlinear set-valued variational inclusions in real Banach spaces. By using the inequality of Petryshyn, the existence of solutions for these kinds of fuzzy nonlinear set-valued variational inclusions without compactness is proved and convergence criteria of iterative sequences generated by the algorithm are also discussed.