  We study the in-medium properties of $D$ and $\bar{D}$ mesons in isospin
asymmetric hyperonic matter arising due to their interactions with the light
hadrons. The interactions of $D$ and $\bar{D}$ mesons with these light hadrons
are derived by generalizing the chiral SU(3) model used for the study of
hyperonic matter to SU(4). The nucleons, the scalar isoscalar meson, $\sigma$
and the scalar-isovector meson, $\delta$ as modified in the strange hadronic
matter, modify the masses of $D$ and $\bar{D}$ mesons. It is found that as
compared to the $\bar{D}$ mesons, the $D$ meson properties are more sensitive
to the isospin asymmetry at high densities. The effects of strangeness in the
medium on the properties of $D$ and $\bar{D}$ mesons are studied in the present
investigation. The $D$ mesons ($D^0$,$D^+$) are found to undergo larger medium
modifications as compared to $\bar{D}$ mesons ($\bar {D^0}$, $D^-$) with the
strangeness fraction, $f_s$ and these modifications are observed to be more
appreciable at high densities. The present study of the in-medium properties of
$D$ and $\bar{D}$ mesons will be of relevance for the experiments in the future
Facility for Antiproton and Ion Research, GSI, where the baryonic matter at
high densities will be produced. The isospin asymmetric effects in the doublet
$D = (D^{0}, D^{+})$ in the strange hadronic matter should show in observables
like their production and flow in asymmetric heavy-ion collisions as well as in
$J/\psi$ suppression.
