We obtain inequalities for statistical submanifolds of a statistical manifold of quasi-constant curvature. We also obtain the Chen–Ricci inequality and the generalized Wintgen inequality for this type of submanifolds.

We consider Kähler-like statistical manifolds, whose curvature tensor field satisfies a natural condition. For their statistical submanifolds, we prove a Chen first inequality and a Chen inequality for the invariant $\delta (2,2)$ .

We consider Einstein statistical warped product manifolds I x f N, M x f N and M x f I; where I, M and N are 1, m and n dimensional statistical manifolds, respectively.