2025/04/23 by Hung Bui The, The, Hung Bui
Computer Science · Economics, Econometrics and Finance · Mathematics · #Optimization and Variational Analysis #Economic theories and models #Advanced Optimization Algorithms Research
paper · pdf · doi:10.48550/arxiv.2504.16497
In this paper, we deal with the following generalized vector equilibrium problem: Let X, Y be topological vector spaces over reals, D be a nonempty subset of X, K be a nonempty set and θ be origin of Y. Given multi-valued mapping F: D× K\rightrightarrows Y, can be formulated as the problem, find x∈ D such that GVEP(F, D, K) θ∈ F( x, y) for all y∈ K. We prove several existence theorems for solutions to the generalized vector equilibrium problem when K is an arbitrary nonempty set without any algebraic or topological structure. Furthermore, we establish that some sufficient conditions ensuring the existence of a solution for the considered conditions are imposed not on the entire domain of the bifunctions but rather on a self-segment-dense subset. We apply the obtained results to variational relation problems, vector equilibrium problems, and common fixed point problems.