Abstract
In this paper, the connectedness of solution sets for generalized vector equilibrium problems via free-disposal sets (GVEPVF) in complete metric space is discussed. Firstly, by virtue of Gerstewitz scalarization functions and oriented distance functions, a new scalarization function $$\omega $$ is constructed and some properties of it are given. Secondly, with the help of $$\omega $$ , the existence of solutions for scalarization problems (GVEPVF) $$_\omega $$ and the relationship between the solution sets of (GVEPVF) $$_\omega $$ and (GVEPVF) are obtained. Then, under some suitable assumptions, sufficient conditions of (path) connectedness of solution sets for (GVEPVF) are established. Finally, as an application, the connectedness results of E-efficient solution set for a class of vector programming problems are derived. The obtained results are new, and some examples are given to illustrate the main results.
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