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<p>In this paper, we examine parametric set-valued equilibrium problems. We begin by introducing a quasiconvexity property for set-valued maps and exploring its relationship with existing concepts. Next, we analyze the semicontinuity and continuity of approximate solution maps for these problems, without assuming the solid condition of the ordered cone and the compact values of the objective map. Finally, we demonstrate an application of the main results to set optimization problems involving a possibly less order relation.</p>

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Semicontinuity conditions for set-valued equilibrium problems and applications to set optimization problems

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Nguyen Huu Danh

摘要

In this paper, we examine parametric set-valued equilibrium problems. We begin by introducing a quasiconvexity property for set-valued maps and exploring its relationship with existing concepts. Next, we analyze the semicontinuity and continuity of approximate solution maps for these problems, without assuming the solid condition of the ordered cone and the compact values of the objective map. Finally, we demonstrate an application of the main results to set optimization problems involving a possibly less order relation.