In [7] a new class of contraction type mappings on probabilistic metric spaces is introduced and a fixed point theorem for such mappings is proved. V. Radu generalized in [14] the fixed point theorem from [7] to $(S,\mathcal F,t)$, which is a complete Menger space with $T$-norm $t$ such that $\sup_{a<1}t(a,a)=1$. In this paper we shall generalize fixed point theorems from [7, 14] and [2].