Abstract Consider an ordered Banach space and f , g f,g two self-operators defined on the interior of its positive cone. In this article, we prove that the equation f ( X ) = g ( X ) f(X)=g(X) has a positive solution, whenever f is strictly α \alpha -concave g-monotone or strictly ( − α ) (-\alpha ) -convex g-antitone with g super-homogeneous and surjective. As applications, we show the existence of positive definite solutions to new classes of nonlinear matrix equations.

中文翻译：

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一类非线性算子的正重合点及其在矩阵方程中的应用

摘要 考虑一个有序的 Banach 空间和 f , gf,g 定义在其正锥内部的两个自算符。在本文中，我们证明方程 f ( X ) = g ( X ) f(X)=g(X) 有正解，只要 f 是严格 α \alpha -凹g-单调或严格 ( − α ) (-\alpha ) -凸 g-反同与 g 超均匀和满射。作为应用，我们展示了新类别非线性矩阵方程的正定解的存在。