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<p>In this paper, we examine parametric vector equilibrium problems in which the objective mappings take values in a linear space. We introduce generalized concepts of semistrict and explicit quasiconvexity for functions. Utilizing these concepts, along with a recent algebraic semicontinuity notion for vector-valued maps and an algebraic version of a non-linear scalarization function, we establish sufficient conditions for the non-emptiness of solution sets and the continuity of solution maps for the reference problems. Our results are novel and different from those previously presented in the literature. An application is provided at the end of the paper.</p>

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Existence and continuity of solutions to vector equilibrium problems via non-linear scalarization

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Ha Manh Linh,
  • Tran Ngoc Tam

摘要

In this paper, we examine parametric vector equilibrium problems in which the objective mappings take values in a linear space. We introduce generalized concepts of semistrict and explicit quasiconvexity for functions. Utilizing these concepts, along with a recent algebraic semicontinuity notion for vector-valued maps and an algebraic version of a non-linear scalarization function, we establish sufficient conditions for the non-emptiness of solution sets and the continuity of solution maps for the reference problems. Our results are novel and different from those previously presented in the literature. An application is provided at the end of the paper.