  We prove versions of Ekeland, Takahashi and Caristi principles in
sequentially right $K$-complete quasi-pseudometric spaces (meaning asymmetric
pseudometric spaces), the equivalence between these principles, as well as
their equivalence to the completeness of the underlying quasi-pseudometric
space.
  The key tools are Picard sequences for some special set-valued mappings
corresponding to a function $\varphi$ on a quasi-pseudometric space, allowing a
unitary treatment of all these principles.
