  In the present paper a generalized K\"ahlerian space $\mathbb{G}\underset 1
{\mathbb{K}}{}_N$ of the first kind is considered, as a generalized Riemannian
space $\mathbb{GR}_N$ with almost complex structure $F^h_i$, that is
covariantly constant with respect to the first kind of covariant derivative.
  Using the non-symmetric metric tensor we find necessary and sufficient
conditions for a geodesic mapping $f:\mathbb{GR}_N\to \mathbb{G}\underset 1
{\mathbb{\bar{K}}}{}_N$ with respect to the four kinds of covariant
derivatives.
