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We investigate the impact of so called kinematic constraint on gluonevolution at small $x$. Implanting the constraint on the real emission term ofgluon ladder diagram, we obtain an integro-differential form of BFKL equation.Later we solve the equation analytically using the method of characteristics.We sketch the Bjorken x and transverse momentum $k_t^2$ dependence of oursolution of unintegrated gluon distributions $f(x,k_t^2)$ in kinematicconstraint supplemented BFKL equation and contrasted the same with originalBFKL equation. Then we extract the collinear gluon density $xg(x,Q^2)$ fromunintegrated gluon distributions $f(x,k_t^2)$ and compared our theoreticalprediction with that of global data fits viz. NNPDF3.1sx and CT14. Finally weassess the sensitivity of $f(x,k_t^2)$ towards BFKL intercept $\lambda$ forthree canonical choices of $\lambda$ viz. o.4, 0.5 and 0.6.

Small $x$ phenomenology on gluon evolution through BFKL equation in light of a constraint in multi-Regge kinematics