Generalized Vector Equilibrium Problems with Relatively Monotone Mappings

Suhel Ahmad Khan

Abstract

In this paper, we consider a generalized vector equilibrium problem overproduct sets in topological vector spaces. We establish that generalized vector equilibriumproblems and a system of generalized vector equilibrium problems have samesolution set. Further we define the concepts of relative pseudo monotonicity and relativelygeneralized B-pseudomontonicity for the set-valued bifunctions. Using theseconcepts and fixed point theorems, we establish some existence results for generalizedvector equilibrium problems and system of generalized vector equilibrium problems.The concepts and results presented in this paper extend and unify a number of knownconcepts and results in the literature.