ABSTRACT In this work we propose a generalization of the notion of directional monotonicity. Instead of considering increasingness or decreasingness along rays, we allow more general paths defined by curves in the n-dimensional space. These considerations lead us to the notion of α-monotonicity, where α is the corresponding curve. We study several theoretical properties of α-monotonicity and relate it to other notions of monotonicity, such as weak monotonicity and directional monotonicity.

中文翻译：

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基于曲线的单调性：方向单调性的推广

摘要 在这项工作中，我们提出了方向单调性概念的概括。我们不考虑沿射线的增加或减少，而是允许由 n 维空间中的曲线定义的更一般的路径。这些考虑使我们想到了 α-单调性的概念，其中 α 是相应的曲线。我们研究了 α-单调性的几个理论性质，并将其与其他单调性概念相关联，例如弱单调性和方向单调性。