Feasibility-solvbility theorems for generalized vector equilibrium problem in reflexive banach spaces
Gang Wang, Haitao Che, Haibin Chen · Fixed Point Theory and Applications · 2012
In this article, the solvability of generalized vector equilibrium problem (GVEP) with set-valued mapping in reflexive Banach spaces is considered. Under suitable conditions, we establish a link between S K and for the GVEP. Furthermore, new sufficient conditions are provided for the nonemptiness and boundedness of the solution set of the GVEP if it is strictly feasible in the strong sense. The new results extend and improve some existence theorems for vector equilibrium problem in some sense. Mathematical subject classification: 49K30; 90C29.