On generalized vector quasivariational-like inequality problems

We introduce a class of generalized vector quasivariational-like in equality problems in Banach spaces. We derive some new existence results by using KKM-Fan theorem and an equivalent fixed point theorem. As an application of our results, we have obtained as special cases the existence results for vector quasi-equilibrium problems, generalized vector quasivariational in equality and vector quasi-optimization problems. The results of this paper generalize and unify the corresponding results of several authors and can be considered as a significant extension of the previously known results.