Normalized Analytic Functions with Fixed Second Coefficient

This paper studies normalized analytic functions f with fixed second coefficient defined on open unit disk for which (1+z)^2f(z)/z and (1+z)f(z)/z are functions having positive real part. The radius of strongly starlikeness, the radius of lemniscate starlikeness, the radius of parabolic starlikeness and other starlikeness radii estimates are calculated for these functions. As well relevant connections of computed radii estimates with the existing one are also shown.