On nonlinear equations for fuzzy mappings in probabilistic normed spaces

Abstract

In this paper, we introduce the concept of probabilistic Ψ-contractor couple, which simplifies and weakens that of probabilistic Φ- g-contractor given by Cho et al. (Fuzzy Sets and Systems 110 (2000) 115–122). By using this concept, we study the existence and iteration convergence of solutions for set-valued nonlinear operator equations and nonlinear equations of fuzzy mappings in Menger PN-spaces. The results presented in this paper improve and extend the corresponding results of Cho et al. in a sense.