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

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  • Meiqiang Feng
  • Xuemei Zhang
  • Weigao Ge

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.

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Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:439137
DOI: 10.1155/2010/439137
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