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Zbl 1214.47051
Liu, Yicheng; Wang, Xiao
(Liu, Yi-cheng;)
Contraction conditions with perturbed linear operators and applications. (English)
[J] Math. Commun. 15, No. 1, 25-35 (2010). ISSN 1331-0623

Let $F$ be a nonempty closed subset of $BC(I,E)$ and $A:F\to F$ be an operator controlled by the contraction conditions with a perturbed linear operator. The authors establish a theorem which ensures that $A$ has a unique fixed point in $F$. The authors also show that some known fixed point theorems concerned with integral operators can be derived from their theorem. In addition, the authors obtain a multivalued version of their theorem. As applications, the existence and uniqueness of solutions of impulsive periodic boundary value problems and functional differential inclusions are exhibited in the last section.
[Long Wei (Jiangxi)]

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
34B37 Boundary value problems with impulses
47N20 Appl. of operator theory to differential and integral equations
47J22
47H04 Set-valued operators

Keywords: fixed point theorem; multi-valued mapping; differential inclusions; periodic boundary value problem

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