In this paper we obtain a general fixed point theorem for an affine mapping in Banach space. As an application of this theorem we study existence of periodic solutions to the equations of the linear elasticity theory.
New fixed point results are presented for maps defined on closed subsets of a Fréchet space \(E\). The proof relies on fixed point results in Banach spaces and viewing \(E\) as the projective limit of a sequence of Banach spaces.
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