Consider an Archimedean partially ordered vector space $X$ with generating cone (or, more generally, a pre-Riesz space $X$). Let $P$ be a linear projection on $X$ such that both $P$ and its complementary projection $I - P$ are positive; we prove that the range of $P$ is a band. This shows that the well-known concept of band projections on vector lattices can, to a certain extent, be transferred to the framework of ordered vector spaces.
Coupled coincidence point theorems for nonlinear contractions in partially ordered metric spaces
在半序度量空间中得到了混合$g$ -单调非线性算子$F:X \times X \rightarrow X$的耦合重合和耦合公共不动点定理。我们的结果是最近的重合点定理由于Lakshmikantham和\' Ciri\' c [Lakshmikantham，V.，\' Ciri\' c，L.，\textit{Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces}，非线性分析\textbf{70}（2009），4341-4349]，Bhaskar和Lakshmikantham建立的耦合不动点定理[T.G. Bhaskar，V. Lakshmikantham，\textit{Fixed point theorems in partially ordered metric spaces and applications}，Nonlinear Anal. \textbf{65}（2006）1379-1393]，并且还包括最近文献中的几个相关结果作为特定病例。
Coupled fixed point theorems for $ϕ$-contractive mixed monotone mappings in partially ordered metric spaces
本文推广了[T.G.]中关于混合单调算子$F:X \times X \rightarrow X$的耦合不动点定理。Bhaskar，V. Lakshmikantham，\textit{Fixed point theorems in partially ordered metric spaces and applications}，Nonlinear Anal. \textbf{65}（2006）1379-1393]和[N. V. Luong和N.X. Thuan，\textit{Coupled fixed points in partially ordered metric spaces and application}，Nonlinear Anal. \textbf{74}（2011）983-992]，通过削弱所涉及的收缩条件。为了说明推广的有效性，还给出了一个例子以及对非线性弗雷德霍姆积分方程的应用.
Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces
本文推广了[T.G.]中关于混合单调算子$F:X \times X \rightarrow X$的耦合不动点定理。Bhaskar，V. Lakshmikantham，\textit{Fixed point theorems in partially ordered metric spaces and applications}，Nonlinear Anal. TMA \textbf{65}（2006）1379-1393]通过显著减弱所涉及的收缩条件来实现。我们的证明技术本质上是不同的，更自然。为了说明推广的有效性，还给出了一个例子以及对周期边值问题的应用。
Coupled fixed point theorems for generalized symmetric Meir--Keeler contractions in ordered metric spaces
本文在半序度量空间中引入广义对称Meir-Keeler压缩，证明了混合单调算子$F:X \times X \rightarrow X$的几个耦合不动点定理.所得结果推广、补充和统一了Samet [B. Samet，\textit{Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces}，非线性分析。\textbf{72}（2010），4508-4517]，Bhaskar和Lakshmikantham [T.G. Bhaskar，V. Lakshmikantham，\textit{Fixed point theorems in partially ordered metric spaces and applications}，Nonlinear Anal. TMA \textbf{65}（2006）1379-1393]和其他一些非常近期的论文。最后给出了一个例子来说明我们的推广是有效的。
Existence and convergence theorems for monotone generalized alpa-nonexpansive mappings in uniformly convex partially ordered hyperbolic metric spaces and its application
