在這篇文章裡，我們將要介紹兩個關於φ-monotone算子的概念。其中一個內容是探討φ-monotone算子的擴張，例如︰Burachik形式擴張 以及Rockafellar形式擴張 。我們將描述擴張系統的一般性質並且找出包含transportation性質的最大的擴張系統。另一個內容是關於不同的φ-monotone算子的和；更明確的說，我們將會介紹一種兩個φ-monotone算子的擴張和，並且說明在某幾種情況下利用maximal φ-monotone的性質，它將會轉變成一般的和。

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