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Zbl 1187.34035
Avery, Richard; Henderson, Johnny; O'Regan, Donal
Four functionals fixed point theorem. (English)
[J] Math. Comput. Modelling 48, No. 7-8, 1081-1089 (2008). ISSN 0895-7177

Summary: The four functionals fixed point theorem is a generalization of the original, as well as the functional generalizations, of the Leggett-Williams fixed point theorem. In the four functionals fixed point theorem, neither the upper nor the lower boundary of the underlying set is required to map below or above the boundary in the functional sense. As an application, the existence of a positive solution to a second-order right focal boundary value problem is considered by applying both standard and nonstandard choices of functionals. An extension to multivalued maps is provided for completeness.

MSC 2000:: *34B18 Positive solutions of nonlinear boundary value problems
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47N20 Appl. of operator theory to differential and integral equations

Keywords: fixed point theorems; compression-expansion; functionals

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