We study the medium modifications of the spectral functions as well as production cross-sections of the strange vector mesons ($phi$, $K^*$ and $bar {K^*}$) in isospin asymmetric strange hadronic matter. These are obtained from the in-medium masses of the open strange mesons and the decay widths $phi rightarrow Kbar K$, $K^* rightarrow Kpi$ and $bar {K^*} rightarrow {bar K}pi$ in the hadronic medium. The decay widths are computed using a field theoretic model of composite hadrons with quark/antiquark constituents, from the matrix element of the light quark-antiquark pair creation term of the free Dirac Hamiltonian between the initial and final states. The matrix element is multiplied with a coupling strength parameter for the light quark-antiquark pair creation, which is fitted to the observed vacuum decay width of the decay process. There are observed to be substantial modifications of the spectral functions as well as production cross-sections of these vector mesons due to isospin asymmetry as well as strangeness of the hadronic medum at high densities. These studies should have observable consequences, e.g. in the yield of the hidden and open strange mesons arising from the isospin asymmetric high energy heavy ion collisions at the Compressed baryonic matter (CBM) experiments at the future facility at GSI.
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