Generalized Strong Vector Equilibrium-Like Problems in
Yali Zhao, Xiaoqing Du · 2009
The purpose of this paper is to study the solvability for a class of generalized strong vector equilibrium-like problems in reflexive Banach spaces. Firstly, utilizing Brouwer’s fixed point theorem, we prove the solvability for this class of generalized strong vector equilibrium-like problems without monotonicity assumption. Secondly, we introduce the new concept of pseudomonotonicity for vector set-valued mapping and prove the solvability for this class of generalized strong vector equilibrium-like problems for pseudomonotone vector set-valued mapping by using Fan’s lemma and Nadler’s theorem. Our results extend and improve the corresponding results in this direction.