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The Palatini $f(R)$ gravity, is able to probably explain the late time cosmicacceleration without the need for dark energy, is studied. In this paper, weinvestigate a number of $f(R)$ gravity theories in Palatini formalism by meansof statefinder diagnosis. We consider two types of $f(R)$ theories: (i)$f(R)=R+\alpha R^{m}-\beta R^{-n}$ and (ii) $f(R)=R+\alpha ln R+\beta$. We findthat the evolutionary trajectories in the $s-r$ and $q-r$ planes for varioustypes of the Palatini $f(R)$ theories reveal different evolutionary propertiesof the universe. Additionally, we use the observational $H(z)$ data toconstrain models of $f(R)$ gravity.

Statefinder diagnosis for the Palatini $f(R)$ gravity theories