Abstract In this article, we first discuss the subduality and orthogonality of the cones and the dual cones when the norm is monotone in Banach spaces. Then, under different assumptions, the necessary and sufficient conditions for the ordering increasing property of the metric projection onto cones and order intervals are studied. Moreover, representations of the metric projection onto cones and order intervals are obtained. As applications, the solvability and approximation results of solutions to nonlinear discontinuous variational inequality and complementarity problems are proved by partial ordering methods.

中文翻译：

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锥体的表征及其在巴拿赫空间中的应用

摘要 在本文中，我们首先讨论了当范数在 Banach 空间中是单调时锥体和对偶锥体的二次性和正交性。然后，在不同的假设下，研究了度量投影到锥体和阶距上的阶次递增性质的充要条件。此外，还获得了在锥体和阶次区间上的度量投影的表示。作为应用，通过偏序方法证明了非线性不连续变分不等式和互补问题解的可解性和逼近结果。