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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2504.16497 |
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| _version_ | 1866910917237669888 |
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| author | The, Hung Bui |
| author_facet | The, Hung Bui |
| contents | 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 $F: D\times K\rightrightarrows Y$, can be formulated as the problem, find $\bar x\in D$ such that $$\mbox{GVEP}(F, D, K)\,\,\,\,\,\,θ\in F(\bar x, y)\ \mbox{for all}\ y\in K.$$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized vector equilibrium problems with pairs of bifunctions and some applications The, Hung Bui Optimization and Control 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 $F: D\times K\rightrightarrows Y$, can be formulated as the problem, find $\bar x\in D$ such that $$\mbox{GVEP}(F, D, K)\,\,\,\,\,\,θ\in F(\bar x, y)\ \mbox{for all}\ y\in K.$$ 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. |
| title | Generalized vector equilibrium problems with pairs of bifunctions and some applications |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.16497 |