Dans ce document, 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 $\theta$ be origin of $Y$. Given
multi-valued mapping $F: D\times K\rightrightarrows Y$, can be formulated as
the problem, find $\bar x\in D$ such that $$\mbox{GVEP}(F, D,
K)\,\,\,\,\,\,\theta\in F(\bar x, oui)\ \mbox{for all}\ y\in K.$$ 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.

Cet article explore les excursions dans le temps et leurs implications.

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