A couple of nonlinear equations with fuzzy mappings in fuzzy normed spaces

In this paper, we introduce the concept of Φ-contractor couple and study the existence of solutions for a couple of nonlinear equations with fuzzy mappings in fuzzy normed spaces. We construct some new iterative algorithms for solving the couple of nonlinear equations with fuzzy mappings and prove the convergence of iterative sequences generated by the algorithms in fuzzy normed spaces. As applications, we obtain some new common fixed point theorems for fuzzy mappings in fuzzy normed spaces. The results presented in this paper improve and generalize corresponding results of Cho et al. (Fuzzy Sets and Systems 110 (2000) 115) and Fang and Song (Fuzzy Sets and Systems 121 (2001) 267).