Vector F-implicit complementarity problems in Banach spaces

In this paper, we introduce a new class of general mixed vector F -implicit complementarity problems and general mixed vector F -implicit variational inequality problems, and study the equivalence between of them under certain assumptions in Banach spaces. We also derive some new existence theorems of solutions for the general mixed vector F -implicit complementarity problems and the general mixed vector F -implicit variational inequality problems by using the FKKM theorem under some suitable assumptions without monotonicity. Moreover, we establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution mapping of the general mixed vector F implicit variational inequality problems. 2000 Mathematics Subject Classification. Primary: 90C33, 49J40.