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Contraction conditions with perturbed linear operators and applications. (English) Zbl 1214.47051
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.

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
34B37Boundary value problems for ODE with impulses
47N20Applications of operator theory to differential and integral equations
47J22Variational and other types of inclusions
47H04Set-valued operators
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