Continuity of the solution mapping to parametric generalized vector equilibrium problems

In this paper, two kinds of parametric generalized vector equilibrium problems in normed spaces are studied. The sufficient conditions for the continuity of the solution mappings to the two kinds of parametric generalized vector equilibrium problems are established under suitable conditions. The results presented in this paper extend and improve some main results in Chen and Gong (Pac J Optim 3:511–520, <CitationRef CitationID="CR9">2010</CitationRef>), Chen and Li (Pac J Optim 6:141–152, <CitationRef CitationID="CR11">2010</CitationRef>), Chen et al. (J Glob Optim 45:309–318, <CitationRef CitationID="CR12">2009</CitationRef>), Cheng and Zhu (J Glob Optim 32:543–550, <CitationRef CitationID="CR17">2005</CitationRef>), Gong (J Optim Theory Appl 139:35–46, <CitationRef CitationID="CR22">2008</CitationRef>), Li and Fang (J Optim Theory Appl 147:507–515, <CitationRef CitationID="CR30">2010</CitationRef>), Li et al. (Bull Aust Math Soc 81:85–95, <CitationRef CitationID="CR31"> 2010</CitationRef>) and Peng et al. (J Optim Theory Appl 152(1):256–264, <CitationRef CitationID="CR33">2011</CitationRef>). Copyright Springer Science+Business Media, LLC. 2013