A contractive mapping on fuzzynormed linear spaces

In this paper, we use the de nition of fuzzy normed spaces given by Bag and Samanta and provide four types of fuzzy versions of contraction. We show that these mappings necessarily have unique xed points in fuzzy normed linear spaces. Moreover we prove that the presented theorems are indeed fuzzy extensions of their classical counterparts.

Keywords:

Fuzzy norm , Fuzzy normed linear space , Fixed point , semi-norm , Contractive conditions