In the present paper a generalized Kählerian space $𝔾{\underset{1}{𝕂}}_N$ of the first kind is considered as a generalized Riemannian space ${\mathrm{𝔾ℝ}}_N$ with almost complex structure $F_i^h$ that is covariantly constant with respect to the first kind of covariant derivative. Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings $f:{\mathrm{𝔾ℝ}}_N\to 𝔾{\underset{1}{\overline{𝕂}}}_N$ with respect to the four kinds of covariant derivatives. These conditions have the form of a closed system of partial differential equations in covariant derivatives...