Revisiting gluon density from the BK equation with kinematical constraint and large x terms

We perform analysis of the small x non-linear evolution equation formulated in momentum space supplemented by higher order terms. The equation is defined in wide range of transverse momentum and longitudinal momentum fraction extending previous studies performed in \cite{Kutak:2003bd,Kutak:2004ym}. The linear part of the equation is motivated by the renormalization group improved small x approach which accounts for resummation of higher orders, and includes collinear splitting function and kinematical constraint. The solution to the equation is then used to perform the fit to Deep Inelastic Scattering reduced cross section data.