In this paper, we introduce three new classes of generalized vector quasi-equilibrium problems. Then by a fixed point theorem we give the existence of solutions to these three ones.

the notion of generalized locally bounded $i$-topological vectorspaces is introduced. some of their important properties arestudied. the relationship between this kind of spaces and thelocally bounded $i$-topological vector spaces introduced by wu andfang [boundedness and locally bounded fuzzy topological vectorspaces, fuzzy math. 5 (4) (1985) 87$-$94] is discussed. moreover, wealso use the fam...

In this paper, we consider strong form of a vector equilibrium problem and establish some existence results for solutions of such problem in the setting of topological vector spaces. We provide several coercivity conditions under which strong vector equilibrium problem has a solution. Our results generalize and extend the results of Bianchi and Pini [Coercivity conditions for equilibrium proble...

The quasi-equilibrium problems with constraints are formulated and some sufficient conditions on the existence of their solutions are shown. As special cases, we obtain several results on the existence of solutions of different vector quasivariational inequality and vector optimization problems. An application of the obtained results is given to show the existence of solutions of quasi-optimiza...