A modified Balitskii-Fadin-Kuraev-Lipatov equation with unitarity

We propose a modified Balitskii-Fadin-Kuraev-Lipatov equation from the viewpoint of the resummation technique, which satisfies the unitarity bound. The idea is to relax the strong rapidity ordering and to consider the variation of the gluon distribution function with the momentum fraction, when evaluating the BFKL kernel. It is shown that the power-law rise of the gluon distribution function with the small Bjorken variable x turns into a logarithmic rise at x→0.