The article relates to generalizations of some aspects of contractions to the so-called cone metric spaces. The cone is assumed solid, which opens the opportunity of the standard scalarization. The main results are analogues of the textbook theorems about Picard iterates. The authors view as the distinction of their analysis the fact that the cones in topological vector spaces they consider may fail to be normal. Reviewer's remark. Analogous general results, free of the interior point assumption, are straightforward within Boolean valued analysis; see, for instance, [\textit{A. G. Kusraev} and \textit{S. S. Kutateladze}, ``Introduction to Boolean-valued analysis'' (in Russian) (Moskva: Nauka) (2005; Zbl 1087.03032)].