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

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-o...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2010-01, Vol.2010 (2010), p.1043-1055
Main Authors: Feng, Meiqiang, Zhang, Xuemei, Ge, Weigao
Format: Article
Language:English
Subjects:
Applied mathematics
Banach space
Banach spaces
Boundary conditions
Boundary value problems
Compressing
Differential equations
Education
Existence theorems
Fixed points (mathematics)
Integrals
Mathematical models
Norms
Operators
Ordinary differential equations
Partial differential equations
Studies
Theorems
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2010/439137