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We perform a calculation for the three body $N \bar{K} K$ scatteringamplitude by using the fixed center approximation to the Faddeev equations,taking the interaction between $N$ and $\bar{K}$, $N$ and $K$, and $\bar{K}$and $K$ from the chiral unitary approach. The resonant structures show up inthe modulus squared of the three body scattering amplitude and suggest that a$N\bar{K}K$ hadron state can be formed. Our results are in agreement withothers obtained in previous theoretical works, which claim a new $N^*$resonance around 1920 MeV with spin-parity $J^P=1/2^+$. The existence of theseprevious works allows us to test the accuracy of the fixed center approximationin the present problem and sets the grounds for possible application in similarproblems, as an explorative tool to determine bound or quasibound three hadronsystems.

Faddeev fixed-center approximation to the $N\bar{K}K$ system and the signature of a $N^*(1920)(1/2^+)$ state