Implications of generalized Frampton-Glashow-YanagidaAnsätzeon neutrino masses and lepton flavor mixing

Possible patterns of the Majorana neutrino mass matrix $M$ with one texture zero and one vanishing eigenvalue are classified and discussed. We find that three one-zero textures of $M$ with $m_1 =0$ and four one-zero textures of $M$ with $m_3 =0$ are compatible with current neutrino oscillation data. The implications of these phenomenological ans$rmddot{a}$tze on the neutrino mass spectrum and the neutrinoless double beta decay are also explored in some detail