  We consider a class of spherically symmetric spacetime to obtain some
interesting solutions in F(R) gravity without matter field (pure gravity). We
investigate the geometry of the solutions and find that there is an essential
singularity at the origin. In addition, we show that there is an analogy
between obtained solutions with the black holes of Einstein-Lambda
-power-Maxwell-invariant theory. Furthermore, we find that these solutions are
equivalent to the asymptotically Lifshitz black holes. Also, we calculate
d^2F/dR^2 to examine the Dolgov-Kawasaki stability criterion.
