Abstract
In this paper, we study the $\varepsilon$-generalized strong vector equilibrium problem ($\varepsilon$-GSVEP) and $\varepsilon$-extended vector equilibrium problem ($\varepsilon$-ESVEP) which can be regarded as approximate problems to the generalized strong vector equilibrium problems (GSVEP). Existence results for $\varepsilon$-GSVEP and $\varepsilon$-ESVEP are established. We also investigate various continuities of the solution mappings of $\varepsilon$-GSVEP and $\varepsilon$-ESVEP, respectively.
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