Generalized Strong Vector Equilibrium-Like Problems in Banach Spaces

The purpose of this paper is to study the solvability for a class of generalizedstrong vector equilibrium-like problems in reflexive Banach spaces. Firstly,utilizing Brouwer’s fixed point theorem, we prove the solvability for this class ofgeneralized strong vector equilibrium-like problems without monotonicity assumption.Secondly, we introduce the new concept of pseudomonotonicity for vectorset-valued mapping and prove the solvability for this class of generalized strongvector equilibrium-like problems for pseudomonotone vector set-valued mappingby using Fan’s lemma and Nadler’s theorem. Our results extend and improve thecorresponding results in this direction.