We suggest a modified form of a unitarized BFKL equation imposing the so-called kinematic constraint on the gluon evolution in multi-Regge kinematics. The underlying nonlinear effects on the gluon evolution are investigated by solving the unitarized BFKL equation analytically. We obtain an equation of the critical boundary between dilute and dense partonic system, following a new differential geometric approach and sketch a phenomenological insight on geometrical scaling. Later we illustrate the phenomenological implication of our solution for unintegrated gluon distribution f(x,k_T^2) towards exploring high precision HERA DIS data by theoretical prediction of proton structure functions (F_2 and F_L) as well as double differential reduced cross section (sigma _r). The validity of our theory in the low Q^2 transition region is established by studying virtual photon–proton cross section in light of HERA data.