Fixed point theorems for decreasing operators in ordered Banach spaces with lattice structure and their applications (Q395215)

Let \(E\) be an ordered Banach space with lattice structure. The following are the main results of the authors: {Theorem 1.} Suppose that \(D\subseteq E\) is bounded and \(A:D\to D\) is a decreasing condensing operator. Then \(A\) has a fixed point in \(D\). {Theorem 2.} Suppose that \(P\subseteq E\) is a normal cone and \(A:E\to E\) is a decreasing condensing operator. Then \(A\) has a fixed point in \(E\). An application of these results to uniformly elliptic differential problems is given.