Positive fixed points for semipositone operators in ordered Banach spaces and applications. (English) Zbl 1290.47051

Zhao, Zengqin; Du, Xinsheng

Abstr. Appl. Anal. 2013, Article ID 406727, 5 p. (2013).

Let \(E\) be a real ordered Banach space with the norm \(\|\cdot \|\), \(P\) a cone of \(E\), and “\(\leq \)” the partial ordering defined by \(P\). The cone \(P\) is said to be normal if there exists a positive constant \(N\) such that \( 0 \leq x \leq y\) implies \(\|x\|\leq N\|y\|\) and is said to be minihedral if \(\sup\{x, y\}\) exists for each pair of elements \(x, y \in\{\mathbb E\}\). The authors study the existence of positive fixed points for semipositone operators in ordered Banach spaces. They also apply their results to Hammerstein integral equations of polynomial type.

Reviewer: Hüseyin Çakalli (Istanbul)

MSC:

47H07	Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47H10	Fixed-point theorems
47N20	Applications of operator theory to differential and integral equations

Keywords:

monotone operators; positive operators; fixed-point theorems; ordered normed spaces

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