Generalized contraction mapping principles in probabilistic metric spaces

Abstract

We give an improvement of Theorem 1 from [2] with a quite different approach, which enable us to prove that the fixed point is also globally attractive. In Theorem 2.11 a further generalization is obtained for a complete Menger space (S, script F sign, T), where T belongs to a more general class of continuous t-norms than in the previous case where T = TM (= min). Theorem 3.2 is a generalization of Theorem 2 from [2]. Thereafter the notion of a generalized C-contraction of Krasnoselski's type is introduced and a fixed point theorem for such mappings is proved. An application in the space S(Ω, script K sign, P) is given.