Ekeland, Takahashi and Caristi principles in preordered quasi-metric spaces

We prove versions of Ekeland, Takahashi and Caristi principles in preordered quasi-metric spaces, the equivalence between these principles, as well their to some completeness results for underlying space. These extend proved S.~Cobza\c{s}, Topology Appl. \textbf{265} (2019), 106831, 22, spaces. The key tools are Picard sequences special set-valued mappings on a space $X$, defined terms preorder function $\varphi$ $X$. Key words: space; spaces; variational principles; Ekeland principle; minimization fixed point; point theorem.