ψ-Contraction and [Formula: see text]-contraction in Menger probabilistic metric space.

The purpose of this paper is to present the definition of [Formula: see text]-contractive mapping and to discuss the relation of [Formula: see text]-contractive mappings and [Formula: see text]-contractive mappings. Furthermore, the generalized [Formula: see text]-contraction mapping principle has been proved without the uniqueness condition. Meanwhile, the generalized [Formula: see text]-contraction mapping principle has been obtained by using an ingenious method.