Positive Fixed Point of Strict Set Contraction Operators on Ordered Banach Spaces and Applications

Meiqiang Feng, Xuemei Zhang and Weigao Ge

Abstract and Applied Analysis, 2010, vol. 2010, 1-13

Abstract:

The fixed point theorem of cone expansion and compression of norm type for a strict set contraction operator is generalized by replacing the norms with a convex functional satisfying certain conditions. We then show how to apply our theorem to prove the existence of a positive solution to a second-order differential equation with integral boundary conditions in an ordered Banach space. An example is worked out to demonstrate the main results.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:439137

DOI: 10.1155/2010/439137

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