Fixed and periodic points in the probabilistic normed and metric spaces

In this paper, a fixed point theorem is proved, i.e., if A is a C-contraction in the Menger space (S, F) and E ⊂ S   be such that A(E)¯ is compact, then A has a fixed point. In addition, under the same condition, the existence of a periodic point of A is proved. Finally, a fixed point theorem in probabilistic normed spaces is proved.