  It is known that there exist no warped product semi-slant submanifolds in
Kaehler manifolds \cite{Sahin}. Recently, Chen and Garay studied
pointwise-slant submanifolds of almost Hermitian manifolds in \cite{CG} and
obtained many new results for such submanifolds. In this paper, we first
introduce pointwise semi-slant submanifolds of Kaehler manifolds and then we
show that there exists non-trivial warped product pointwise semi-slant
submanifolds of Kaehler manifold by giving an example, contrary to the
semi-slant case. We present a characterization theorem and establish an
inequality for the squared norm of the second fundamental form in terms of the
warping function for such warped product submanifolds in Kaehler manifolds. The
equality case is also considered.
