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, issue 1
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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https://doi.org/10.1155/2010/439137
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:439137
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