  In this work, we provide a q-generalization of flexible algebras and related
bialgebraic structures, including center-symmetric (also called antiflexible)
algebras, and their bialgebras. Their basic properties are derived and
discussed. Their connection with known algebraic structures, previously
developed in the literature, is established. A q-generalization of Myung
theorem is given. Main properties related to bimodules, matched pairs and dual
bimodules as well as their algebraic consequences are investigated and
analyzed. Finally, the equivalence between q-generalized flexible algebras,
their Manin triple and bialgebras is established.
